Question

Give the derivative of f(x) = arctan(e^(5x)) at the point where x=0

Answer 1

$f(x)=\arctan e^{5x}$
$f'(x)=\dfrac{(e^{5x})'}{1+(e^{5x})^2}=\dfrac{5e^{5x}}{1+e^{10x}}$
$f'(0)=\dfrac5{1+1}=\dfrac52$