Differentiation of e^sinx | Differentiate e^sinx

The differentiation of e^sinx is equal to cosx esinx. In this post, we will learn how to differentiate e^sinx with respect to x.

How to differentiate e^sinx

Let us find the derivative of esinx with respect to x.

Find the derivative of esinx

Question: How to differentiate esinx?


Let y= esinx

Taking natural logarithms i.e. loge both sides, we get that

log y = sinx as we know that logeek =k.

Now, differentiate both sides with respect to x. So we get that

$\dfrac{1}{y} \dfrac{dy}{dx}$ = cosx

⇒ $\dfrac{dy}{dx}$ = y cosx

Putting the value of y, that is, y=esinx, we get that

$\dfrac{d}{dx}$(esinx) = esinx cosx.

Thus, the differentiation of esinx with respect to x is equal to esinx cosx.

Video solution:


Derivative of arc(cotx): The derivative of arc(cotx) is -1/(1+x2).


Q1: What is the derivative of esinx?

Answer: The derivative of e^sinx is equal to cosx esinx.

Q2: If y=esinx, then find dy/dx?

Answer: If y=esinx, then dy/dx = cosx esinx.

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