`f(x) = 6(x^3 + 4)^3` Find the second derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 86 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- If y = x^n ; where n = constant ; then dy/dx = n*x^(n-1)

Now, 

`f(x) = 6(x^3 + 4)^3`

`thus, f'(x) = 6*3*3(x^2)*(x^3+4)^2`

`or, f'(x) = 54(x^2)(x^3 + 4)^2`

Differentiating again w.r.t 'x' we get

`f''(x) = 108x(x^3 + 4)^2 + 54*2*3(x^2)*(x^2)*(x^3 + 4)`

`or, f''(x) = 108x(x^3 + 4)^2 + 324*(x^4)(x^3 + 4)`

`or, f''(x) = 108x(x^3 + 4)[x^3 + 4 + 3x^3]`

`or, f''(x) = 108x(x^3 + 4)[4(x^3 + 1)]`

`or, f''(x) = 432x(x^3 + 4)(x^3 + 1)`

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