Beginner having trouble taking derivative

[Heinz21]

Hello, i am having trouble taking the derivative of functions with using the chain rule plus another rule such as the product rule... i know how to do chain rule by it self and product rule by itself but i am having trouble using them together.. here is an example
g(x)= ( 1+4x )⁵ ( 3+x-x² )⁸

 

[mathman]

Let f(x)=(1+4x)⁵ and h(x)=(3+x-x²)⁸

The g(x)=f(x)h(x) and g'(x)=f(x)h'(x) + f'(x)h(x)

Can you do the rest yourself?

 

[paulfr]

What Mathman is saying is that you first must use The Product Rule for Differentiation.
Then each derivative [h ' (x) and f ' (x) ] will require using The Chain Rule.