# How do you differentiate f(x)=sin(6x+5x^2+1) using the chain rule?

Oct 29, 2015

I found: $f ' \left(x\right) = \left(10 x + 6\right) \cos \left(6 x + 5 {x}^{2} + 1\right)$
First you derive $\sin$ as it is and then multiply by the derivative of its argument:
$f ' \left(x\right) = \textcolor{red}{\cos \left(6 x + 5 {x}^{2} + 1\right)} \cdot \textcolor{b l u e}{\left(6 + 10 x\right)} =$
$= \left(10 x + 6\right) \cos \left(6 x + 5 {x}^{2} + 1\right)$