Need help finding derivative?

Question

Need the f'(x) of the following equations:

A.f(x)=x^2(x-4)^2

B. f(x)=x^2(x-5)^3

I am trying to use the power rule to do this but I think I am simplifying the original equation wrong or something. Help please.

Answer 1

Question A
f (x) = x ² (x - 4) ²
f `(x) = (2 x )(x - 4) ² + 2(x - 4)( x ²)
f `(x) = x (x - 4) [ 2 (x - 4) + 2 x ]
f `(x) = x ( x - 4 ) [ 4 x - 8 ]
f `(x) = 4 x ( x - 4 ) ( x - 2 )

Question B
f (x) = x ² ( x - 5 ) ³
f `(x) = 2 x ( x - 5 ) ³ + 3 ( x - 5 ) ² ( x ² )
f `(x) = x ( x - 5 ) ² [ 2 (x - 5) + 3 x ]
f `(x) = x (x - 5)² (5x - 10)
f `(x) = 5 x (x - 5) ² (x - 2)

Answer 2

What you have are a pairof functions multiplied together. Remember frm the Chain rule that if
f(x) = g(x) * h(x) then
f'(x) = g(x) * h'(x) + g'(x) * h(x)
In the 1'st one, let g(x)=x² and h(x) = (x-4)² then
g'(x) = 2x and h'(x) = 2(x-4) fo that
f'(x) = x²(2(x-4)) + 2x(x-4)² and maybe simplify it a bit.

Doug

Answer 3

a) f(x) = x^2(x-4)^2
f(x) = [x(x-4)]^2
f(x) = (x^2-4x)^2
f'(x) = 2(x^2-4x)(2x-4)
f'(x) = 4x(x-4)(x-2)
b) f(x) = x^2(x-5)^3
f'(x) = (2x)(x-5)^3 + 3(x-5)^2(x^2)
f'(x) = x(x-5)^2 [(2)(x-5) + (3x)]