Can someone show me a step-by-step explanation of this?

Question

anonymous · Answer

derivative of arctan(x+1)

anonymous · Answer

@luvalpaca

anonymous · Answer

$$\frac{d}{dx}\arctan(x)]=\frac{1}{x^2+1}$$
replace $x$ by $x+1$and you will have your answer

anonymous · Answer

oh I see! So do I always have to do this for trig and inverse trig functions?

anonymous · Answer

i am not sure what you mean

anonymous · Answer

it is the case for any composite function 
$$(f(g(x))'=f'(g(x))\times g'(x)$$ in your case $f(x)=\arctan(x)$ and $g(x)=x+1$ 
also $g'(x)=1$ so you really don't have to do anything but replace $x$ by $x+1$

anonymous · Answer

That's what I meant^ the whole substituting thing. Anyways thank you! so much! you helped me understand it!

anonymous · Answer

if it was $\frac{d}{dx}\arctan(x^2)$ then the answer would be $\frac{2x}{x^4+1}$

anonymous · Answer

yw