Question

find the derivative of e^(tan-1(x))

Answer 1

e^(tan^(-1)x)

Answer 2

Use chain rule here
\[\frac{d}{dx} (f(gx))=f'(x) \times \frac d {dx } g(x)\]
Can you try @aprilanahi ?

Answer 3

Wow! That was an interesting effort...

If \( y = e^{atan(x)}\), then \(ln(y) = atan(x)\).

Implicit differentiation provides: \(\dfrac{y'}{y} = \dfrac{1}{1+x^{2}}\)

And we are done. \(y' = \dfrac{e^{atan(x)}}{1+x^{2}}\)