Differentiation of e^cosx | Differentiate e^cosx

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

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

Find the derivative of ecosx

Question: How to differentiate ecosx?

Solution:

Let y= ecosx

Taking natural logarithms on both sides, we get that

logy = cosx [here we use the logarithm formula logeem =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=ecosx. By doing so we obtain that

$\dfrac{d}{dx}$(ecosx) = -ecosx sinx.

Thus, the differentiation of ecosx with respect to x is equal to -ecosx sinx.

Video solution:

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

Derivative of esinx: The derivative of esinx is cosx esinx.

FAQs

Q1: What is the derivative of ecosx?

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

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

Answer: If y=ecosx, then dy/dx = -sinx ecosx.