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,
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