Derivative of e to the Power Tanx

We know the derivative of ex, which is ex.

(ex)' = ex

We can find the derivative of etanx using chain rule.

If y = etanx, find ᵈʸ⁄d.

y = etanx

Let u = tanx.

Then, we have

y = eu

Now, y = eu 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 = eu and u = tanx.

Substitute u = tanx.


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