Derivative of e to the Power Cosx

We know the derivative of ex, which is ex.

(ex)' = ex

We can find the derivative of ecosx using chain rule.

If y = ecosx, find ᵈʸ⁄d.

y = ecosx

Let t = cosx.

Then, we have

y = et

Now, y = et and t = cosx. That is, y is a function of t and t is a function of x.  

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

Substitute y = et and t = cosx.

Substitute t = cosx.


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