find-the-derivatives-of-the-given-functions-rtan-sin-2-pi-theta-3

Question

Find the derivatives of the given functions.
$$r=	an (\sin 2 \pi 	heta)$$

Tyler Moulton · Accepted Answer

we want to find do I. D. S. For the function? Why is equal to the tangent of sign of two PX. In this problem, we&#x27;re going to use a derivative shortcuts. So we picked up for a single variable calculus in particular. We&#x27;re going to make use of the trigonometry derivatives that we&#x27;ve recently learned. So I&#x27;ve listed all six trigonometry derivatives here in particular. We&#x27;re obviously going to need to use sign derivative which is co sign X. And the tangent derivative which is you cant squared X. We&#x27;ll also need to make use of the chain rule to solve so why is already written in the form that&#x27;s most easily differentiable or the simplest form? Thus we can proceed straight to the derivative. So we&#x27;re going to first apply the chain rule. We&#x27;re gonna take the derivative of tangent with respect to what&#x27;s inside and then we&#x27;re gonna take the riverboats inside. So do I. D. X. Is you can&#x27;t square designed by X. Times the derivative signed two PX which is co signed by excuse to pop, thus moving our constant outfront. Our solution is DY DX equals two pi coastline to pi X. Times you can&#x27;t squared sine two PX.

Robert Daugherty · Answer

section 3.6 number 45 We&#x27;re dealing with derivative that requires to know the chain role. So we&#x27;re asked to find the derivative our prime, as a function of Fada. So this is gonna be the product rule. You&#x27;ve got two different functions multiplied. So what we want to do first is let&#x27;s take the derivative of the first term. So the derivative of sine squared. So what&#x27;s the derivative sign is the coastline. So this is gonna be the co sign of data squared Now, what is the derivative of Data Square? That&#x27;s to thinner times. The co sign of two things was product rules. So this is you think that this is f and G, and this is F prime G plus G prime F. So plus the derivative of the second term. So the derivative of the co sign is minus sign of tooth Ada, the derivative of Tooth Ada is going to be too times the sign of data squared and the trouble just a little bit of organization that can go on here. So final answer r squared of Fada is going to be equal to toothache. The co sign of they the squared the co sign of tooth data and then minus two sign of data squared sign of two data and that is your final answer.

Robert Daugherty · Answer

sex in $3 6 problem 46 here were asked to find the derivative and we&#x27;re using chain rule in this case will also be using the product rule because I have two functions that are multiplied. So my derivative, our prime as a function of data. Um, what I&#x27;m gonna do first is let&#x27;s take the derivative of this first term. So the derivative of the seeking ISS, the seeking times, the tangent. So it&#x27;s going to be the seeking of the square root of fada times the tangent of the square root of fada times What is the derivative of the square root of data That&#x27;s 1/2 square root of data times the other term, which is tangent one over theta. So it was the derivative of this term times this term. Now, what would take the derivative of this term times a second term. So it&#x27;s gonna be plus with the derivative the changes that seeking squared. So this is going to be the sequence squared of one over theta times, the derivative of one over a theta. So that&#x27;s gonna be minus one over data squared. And in times this first term, which is seeking the square root of theta. And now what do I have in common? In both terms, it looks like I&#x27;ve got a seeking of theta. So this answer is going to be the sequence of the square root of data. That&#x27;s the only term that I can factor out. And then it looks like I&#x27;ve got one over to square root of Fada tangent, square root of data tinge. It won over theta and then minus. Uh, that&#x27;s gonna be, um, won over. They just squared, seeking squared of one over data and that is our final answer.

Bobby Barnes · Answer

we want to find derivative. Oh R is too two times one over this food if they don&#x27;t plus the square root of think So what I&#x27;m going to do first is rewrite this as power. So we know how to take care of this. There will be two time So called square root is on half power. Invensys, a dominator will be dated to the negative one half and then this isthe dated to be one half. So if we take the derivative of this, we can use the sum and scaler property of derivatives, Two tickets. So we have our prime is equal to so the DD dada. Oh, two times a day to the negative, one half cross to the one half. So first we can go ahead and pull that too out by using the constant property. So he d data both data to the negative One half is a negative one house a month Ada to the one house. Then we can use thie some property to write us too times dd Oh, gonna go ahead and make sure I have my practice is here. They did to the negative on half. Well, the derivative with respect to data. Oh, they want half now. The derivative of each of these will be powerful. We could take negative one half, move it up front some truck off of it. So this will be two times so negative one half then you know, such truck team one off there will be negative three halves. Well, us So we&#x27;LL do the same thing here. One half goes up, subtract one off the power and we&#x27;LL have one half time&#x27;s beta of instructing while that will be negative one half. So I&#x27;m going to go ahead and should be that too in and doing that, will you? Negative data to the negative three helps plus later to the negative one half. And if we want, we can go ahead and rewrite this as fractions, so negative one over will be fatal. So this is gonna be cute and then the square root of it, plus one over the square root of So either of these forms here are sufficient ways to write history

Robert Daugherty · Answer

Section three That six. Problem number 43. So we&#x27;re dealing with functions and being a Mitic, the derivative using the chain rule. So in this case, f prime of theta, the first derivative is going to be start using power rules with two times the sign of data over one, plus the co sign of data race to the first power. Now, times the derivative of everything that&#x27;s inside the parentheses. Well, that&#x27;s gonna involve the quotient rule. So that&#x27;s going to be the derivative of the numerator co science data times the denominator one plus coasts and data minus. And then it&#x27;s the derivative of the denominator, which is minus sign of data times the numerator, which is sign of data. And then all of this over the denominator squared. So the calculus is over, and it&#x27;s into trick identities and algebraic simplification. So this is to sign of data over one plus co sign of Dana Times. Let&#x27;s just expand everything you see there. You&#x27;ve got the co sign of data plus Cosan squared of theta and then plus sine squared of theta over one plus co sign of data quantity squared. Now what? You notice here you&#x27;ve got this sign. Square plus coast on squared, That is equal toe one. So there&#x27;s simplifies to To Scient, Ada over one plus co sign of data times. You&#x27;re gonna have one plus co sign if they don&#x27;t divided by one plus coast on if they two squared. And so what you see here is a simplification here. And then you see, my final answer is F prime of data is equal to two scientific data over one plus co sign of data squared.

Robert Daugherty · Answer

section $3 6 Problem number 27 here were asked to find derivatives malfunction that involved, as needed to know the chain role. So here I need to find the derivative of our so our prime with respect to theta. So the first thing I&#x27;ll use will be the power rule. So this is negative. One times coasts, he can fade up, plus coach engine of failure to the negative to power times the derivative of everything that&#x27;s in this parentheses. So the derivative of the coast seeking is going to be, um this could be what, um, minus co tangent X Cosi connects. The derivative of the co tangent is just simply minus co seeking squared of X. Now, here&#x27;s the thing. Calculus is all complete. We&#x27;re into trig and algebra, usually at this point trying not to make mistakes with either of those. So what do I have here? So it looks like if I put everything together, um, So it looks like I&#x27;ve got um looks like I&#x27;ve got co tangent X co seeking X plus co seeking squared of X. All of that over Cosi can. Sorry, I&#x27;ve mixed up things. Just go back. Um everything is in terms of fatal. So nothing was wrong with the trick part, which is to be precise contends that data cause he can&#x27;t fade up minus co think squared of data. So everything is in terms of the terrible thing. Eso simplifying this. This becomes less. You have got a negative one that could be factored out here with the negative one. That&#x27;s gonna be positive. You&#x27;re gonna have co tangent. Fada Coast, seeking of fado plus CO ck in squared of theta over co seeking of Fada was continued of fada squared in this numerator I could factor out a coast seeking of Fada and then you&#x27;re left with what co changing of data plus coast Seeking of data over co seeking of data, it&#x27;s co tension of data squared. And now what? You look at this particular quantity co change a plus co ck. You&#x27;ve got two in the denominator one in the numerator That&#x27;s going to simplify to just finally co seeking of data over co seeking of Fada plus Co changing of data, which is your final answer

Problem

Find the derivatives of the given functions. $$y=…

Problem 29 Easy Difficulty

Find the derivatives of the given functions.
$$r=\tan (\sin 2 \pi \theta)$$

Answer

$\frac{d r}{d \theta}=2 \pi(\cos 2 \pi \theta) \sec ^{2}(\sin 2 \pi \theta)$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{d r}{d \theta}=2 \pi(\cos 2 \pi \theta) \sec ^{2}(\sin 2 \pi \theta)$

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus