Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Prove that $\frac{d}{d x}(\sec x)=\sec x \tan x$

First write sec $x$ as $\frac{1}{\cos x}$ then differentiate using quotient rule.

Calculus 1 / AB

Chapter 3

Derivatives

Section 4

The Product and Quotient Rules

Oregon State University

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:59

Prove that $\frac{d}{d x}(…

04:20

Prove that $$\frac{d}{…

03:45

Proof $\quad$ Prove that $…

00:40

Prove the identity.$$\…

01:05

04:51

Prove that $$\frac{d}{d x}…

00:41

01:44

Proof of $\frac{d}{d x}(\c…

00:49

$$\text { Prove the identi…

01:28

Assuming that $(d / d x)(\…

we want to prove that the derivative with respect to X d over DX of the function, seek and X is equal to seek inns X times Tangent X Well, let's just try the most direct approach by just taking the derivative of Seek and X well, the derivative of seeking Ex. It might be easier to first right out in terms of signs and coastlines. Seeking X is one over co sign X, and when you see that you might be tempted to use the quotient rule. But that's one of the more complicated derivative rules. And if you see that instead, you can write this as co sign next to the minus one. Then it becomes easier to differentiate. So we have co sign X to the minus one. This is a composition of functions. It has an inter function co sign X, and it has the outer function of raising co sign next to the minus one. So by the change by the chain rule, the first thing we do is we take the derivative of the outer function, raising costa next to the minus one, which by the power rule, tells us that we bring the minus one down and, uh um subtract one from the exponents of coastline X. So from minus one, it becomes a minus two. And now again by the chain rule, we multiply by the derivative of the Inter Function CO sign X, which is minus sine X, and we can simplify this a bit. We have two minus signs So those cancel out and we end up getting sign X over co sign Squared X and we want to get seeking access times Tangent X Well, we can get a sequined by bringing out one of the co signs in the denominator one of her co sign X And then what do we have left? You are left with precisely sign over co sign and thus we get seeking ex Tangent X. We can write a little box two in form the reader that we have reached the end of the proof

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Prove that $\frac{d}{d x}(\csc x)=-\csc x \cot x$

Prove that $$\frac{d}{d x}(\csc x)=-\csc x \cot x$$

Proof $\quad$ Prove that $\frac{d}{d x}[\cos x]=-\sin x$

Prove the identity.$$\tan x \csc x=\sec x$$

Prove that $\frac{d}{d x}(\cot x)=-\csc ^{2} x$

Prove that $$\frac{d}{d x}(\cot x)=-\csc ^{2} x$$

Prove the identity.$$\sec x \cot x=\csc x$$

Proof of $\frac{d}{d x}(\cos x)=-\sin x$ Use the definition of the derivativ…

$$\text { Prove the identity.}$$$$\tan (\pi-x)=-\tan x$$

Assuming that $(d / d x)(\sin x)=\cos x$ and $(d / d x)(\cos x)=$$-\sin …

02:45

Bacteria population The number of bacteria after $t$ hours in a controlled l…

03:12

Differentiate.$y=\frac{1+\sin x}{x+\cos x}$

Differentiate $f$ and find the domain of $f$ $$f(x)=\frac{\ln x}{x^{2}},…

06:18

Find the 1000 th derivative of $f(x)=x e^{-x}$

04:35

29. Dialysis The project on page 458 models the removal ofurea from the …

09:01

Find the limit. Use l'Hospital's Rule where appropriate. If there …

01:08

Solve the differential equation.$$\frac { d u } { d r } = \frac { 1 + \s…

02:39

Differentiate.$f(x)=\frac{1-x e^{x}}{x+e^{x}}$

00:45

Relative change in blood flow Another law of Poiseuille says that when blood…

04:15

Find the derivative of the function using the definition of a derivative. St…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.