I need help understanding how to derivate this function:
$$f(x) = x^{\arctan(x)}$$.
Any suggestions?
I need help understanding how to derivate this function:
$$f(x) = x^{\arctan(x)}$$.
Any suggestions?
Let $f(x) = x^{\arctan{x}}$ then $\log{f(x)} = \arctan{x} \cdot \log x$. Therefore $$\frac{1}{f(x)} \times f'(x) = \frac{d}{dx} \Bigl[ \arctan{x} \cdot \log x \Bigr] \Longrightarrow f'(x) = f(x) \times \frac{d}{dx} \Bigl[ \arctan{x} \cdot \log x \Bigr]$$
HINT $\ \ g^{\:h}\ =\ e^{h\: \log(g)}\:.\ $ Or, take logs, cf. logarithmic derivative, and my post here.