Differentiate y=x(x4+5)3

Question

d/dx = [x(x4+5)3]
d/dx = [f(x)g(x)] = f(x)g’(x)+g(x)f’(x)
d/dx = [x(x4+5)3] = x • d/dx (x4+5)3 + (x4+5)3 • d/dx x
g’(x) = d/dx (x4+5)3 = 3(x4+5)2 • 4x
f’(x) = d/dx (x) = 1
= (x) • 3(x4+5)2 • 4x + (x4+5)3 • 1 (factor out the common form (x4+5)2 )
= (x4+5)2 [(x)(3)(4x)+ (x4+5)]
=(x4+5)2 (12x2+x4+5) (answer I got)

The right answer =(x4+5)2 (13x4+5)
Just trying to see where I went wrong.

Answer 1

Shouldn't g'= 3(x^4+5)^2 * 4x^3 ?

Answer 2

It is hard to read your work with the exponents not raised or indicated by a ^ symbol. There is a mistake where you take the derivative of (x^4+5)^3. You used the "function of a function" or "chain" rule incorrectly.
Here is what I get:

y = x(x^4 +5)^3
Let f(x) = x and g(x) = (x^4+5)^3
dy/dx = (x^4+5)^3 + 3x(x^4+5)^2*4x^3
= (x^4+5)^2 *[(x^4+5) + 12x^4]
= (x^4+5)^2 *(13x^4+ 5)

Answer 3

8 . 4
- - 2 = -
6 . 3