Question

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

Answer 1

derivative of arctan(x+1)

Answer 2

@luvalpaca

Answer 3

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

Answer 4

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

Answer 5

i am not sure what you mean

Answer 6

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 \(x+1\)

Answer 7

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

Answer 8

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

Answer 9

yw