math-check my work

Differentiate y=x(x4+5)3
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.

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

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  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)

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  3. 8 . 4
    - - 2 = -
    6 . 3

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