Differentiation of e^cosx | Differentiate e^cosx

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

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

Find the derivative of e^cosx

Question: How to differentiate e^cosx?

Solution:

Let y= e^cosx

Taking natural logarithms on both sides, we get that

logy = cosx [here we use the logarithm formula log_ee^m =m]

Differentiating both sides with respect to x, we get that

$\dfrac{1}{y} \dfrac{dy}{dx}$ = -sinx

⇒ $\dfrac{dy}{dx}$ = -y sinx

Now we put the value of y, that is, y=e^cosx. By doing so we obtain that

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

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

Video solution:

ALSO READ:

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

Derivative of e^sinx: The derivative of e^sinx is cosx e^sinx.

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