Differentiate (x^2-4x+2)(5x^3-x^2+5)

Question

anonymous · Answer

$$Differentiate (x ^{2}-4x+2)(5x ^{3}-x ^{2}+5)$$

anonymous · Answer

product rule for this one 
use 
$$(fg)'=f'g+g'f$$ with 
$$f(x)=x^2-4x+2, f'(x)=2x-4,g(x)=5x^3-x^2+5,g'(x)=15x^2-2x$$

anonymous · Answer

It says the answer should be $$25x ^{4}-84x ^{3}+42x ^{2}+6x-20$$

anonymous · Answer

f=x2-4x+2
g=5x3-x2+5
f'=2x-4
g'=15x2-2
multiply gf'+fg' answer will be 25x4-84x3+42x2+6x-20

anonymous · Answer

How did you get f=2x+4 and g=15x2-2 ?

anonymous · Answer

Can you break it down so I can try to understand? I'm sorry, I'm having a hard time. :(

anonymous · Answer

if u differentiate ax^y then you get ayx^y-1

anonymous · Answer

so x^2 when differentiated u get 2x

anonymous · Answer

How do you differentiate it from $$x ^{2}-4x+2$$  to that 2x+4 ?
How do you diffferentiate it from $$5x ^{3}-x ^{2}+5$$ to $$15x ^{2}-2$$ ?