Differentiation of e^sinx | Differentiate e^sinx

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

Let us find the derivative of e^sinx with respect to x.

Find the derivative of e^sinx

Question: How to differentiate e^sinx?

Solution:

Let y= e^sinx

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

log y = sinx as we know that log_ee^k =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=e^sinx, we get that

$\dfrac{d}{dx}$(e^sinx) = e^sinx cosx.

Thus, the differentiation of e^sinx with respect to x is equal to e^sinx cosx.

Video solution:

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

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