Find the derivative of $\sin { \left( 3{ x }^{ 2 }+x \right) } $ How do you find the derivative of

$$\sin { \left( 3{ x }^{ 2 }+x \right)  } $$ 

using the derivative definition and not the chain rule.
This is how far I was able to get
Any help would be appreciated. Thanks!

Select $u=3x^2+x\Rightarrow \frac{du}{dx}=6x+1$ then $$\frac{d}{dx}(\sin(u))=\frac{du}{dx}\cos(u)=(6x+1)\cos(3x^2+x)$$
