(x+3)^2(2x-1)^5
how would differentiate using product rule and simplify

Question

(x+3)^2(2x-1)^5
 how would differentiate using product rule and simplify

anonymous · Answer

$$(x+3)^{2}(2x-1)^{5}$$
$$2(x+3)*1*(2x-1)+(x+3)*5(2x-1)^{4}*2$$


you need to apply product rule and chain rule. 
now just simplify.

anonymous · Answer

product rule is where
f'(x)g(x)+f(x)g'(x)

anonymous · Answer

and chain rule is when you have a composite of functions. Eg $$f(g(x))$$

anonymous · Answer

i got up to that part but im having troubles in simplifying it - the answer was 14(x+3)(x+2)(2x-1)^4
i dont know how they got 14

anonymous · Answer

Trying to simplify that would make your work a bit tedious.

anonymous · Answer

i agree. but have no choice its part of the curriculum

anonymous · Answer

But that answer doesn't seem right, it's missing a plus sign

anonymous · Answer

This is what you should have

anonymous · Answer

$$2(x+3)(2x-1)^5 + (x+3)^2 5(2x-1)^4)2$$

anonymous · Answer

yup that is the answer but you have to simplify it so it looks like this 
14(x+3)(x+2)(2x-1)^4