Derivative of e to the Power Tanx

We know the derivative of e^x, which is e^x.

(e^x)' = e^x

We can find the derivative of e^tanx using chain rule.

If y = e^tanx, find ᵈʸ⁄dₓ.

y = e^tanx

Let u = tanx.

Then, we have

y = e^u

Now, y = e^u and u = tanx. That is, y is a function of u and u is a function of x.  

By chain rule, the derivative of y with respect to x,

Substitute y = e^u and u = tanx.

Substitute u = tanx.

Therefore,

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.