## aprilanahi Group Title find the derivative of e^(tan-1(x)) one year ago one year ago

1. aprilanahi

e^(tan^(-1)x)

2. ash2326

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

3. tkhunny

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. $$y' = \dfrac{e^{atan(x)}}{1+x^{2}}$$