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⁄dₓ.
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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