find-the-derivative-of-the-following-functions-yex-csc-x

Question

Find the derivative of the following functions.
$$y=e^{x} \csc x$$

Maurizia De Palma · Accepted Answer

So this problem assets to find the derivative of eating the X times kusi can&#x27;t of X and because we have two different functions being multiplied together, we want to use the product rule which is in the red on the right hand side. So to start, we want to define our A and B terms. So our a is eating the X and the derivative of E. The X is always either the ex and our be is Cosi can&#x27;t of eggs and be crime. If you look up a formula, she or if you know you&#x27;re triggered Andes is cosi can&#x27;t of x co tangent of X and this is negative. So now we can plug these terms into this formula here so we&#x27;ll get why Prime equals you. The x times kusi can&#x27;t of X close into the X times negative Cosi can&#x27;t of x co tangent and X And what you notice is that old terms haven&#x27;t even the X Cosi can&#x27;t in them so we can factor that out so well. Factor out e small factor out e to the X Cosi can&#x27;t of X and what we&#x27;re left is this will send this first term will simplify toe one and we&#x27;re left with co tangent of X in this second term

Jonathon Brumley · Answer

we&#x27;re gonna be looking at a product rule derivative here. It is important to recognize that we have one quantity. Were the variables in the power in another quantity where the very bull is in the base. So we are going to use the product rule. We&#x27;ll go first times the derivative of the second. Now, since you haven&#x27;t X to the e power, that&#x27;s going to use X to a constant power rule, which means bring the power out front. Subtract one from the old power And then, for the second part of the derivative, we go second term times the derivative the first, which is hey to the X. Now we could rewrite that a little bit if we want to. Ah, we do have eat of the x times and eat of the first in that first part so you could add the powers ending with e to the X plus one times X to the minus one plus e to the x Times X to the e power

Philip Christensen · Answer

to calculate the derivative of the function X to the We need to remember the rule of dealing with X rays to a power. So the derivatives, any X rays to a constant and it&#x27;s equal to and times X to the n minus one power. So this is very quick. F Prime X is equal to e, since he is a constant top eight times acts to the E minus one and since he is a constant today, your regular number, we don&#x27;t have to expand that unless you want to round, so we can just leave it in its simplest form like match.

Amy Jiang · Answer

since you don&#x27;t win the part of two terms here. So let&#x27;s take our derivative by using the product role for you. Derivative of X. That&#x27;s one times are meaning of plus derivative of E. That&#x27;s negative. You, too, Negative X and in time, this is our fault conservative.

Romaila Saud · Answer

In order to find the de innovative off function, Why equals Go seek And I need to the power acts we first need Teoh identify the inner and outer function. The inter function in this case is going to be U equals e to the Power X whereas the outer function why is going to be go seek and are for you Next we need to identify the Dara Vader&#x27;s of each of those equations hands Do you, by the X is going to be equal to E of efs where as de wife i d you is going to be equal to negative Go seek and you cost you by change Will we know that divide by the eggs is equal to de vie vie de you do do you buy the X? All they have to do now is to put in the values that we&#x27;ve already evaluated. Hence the equation becomes negative Kaseke and you got a few into u to the Power X. Next we put in the value off you in our equation and simply five. The final answer becomes negative g to the power axe into good seeking and e to the Power X caught he to the Power X hence the final answer

Jonathon Brumley · Answer

we have a relatively straightforward problem here. It is key that you do not trying to separate or expand this original log because there is no separation or expansion if you have the natural log of a plus B. So all we need to do to take the derivative is to put the D you over you. So put that you on bottom e to the X plus e to the negative X. It&#x27;s derivative on top. Derivative is eating the X and the derivative of eat of the negative acts is negative e to the negative X people.

Problem

Find the derivative of the following functions. $…

Problem 45 Medium Difficulty

Find the derivative of the following functions.
$$y=e^{x} \csc x$$

Answer

$e^{x}$ csc x (1 - cot x)

Related Courses

Calculus Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Kristen K.

Michael J.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals

Grace H.

Kristen K.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$e^{x}$ csc x (1 - cot x)

Calculus Early Transcendentals

Grace H.

Kristen K.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

William Briggs, Lyle Cochran, Bernard GilletCalculus Early Transcendentals

Grace H.

Kristen K.

Michael J.

Joseph L.

William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals