What is the derivative of (x^4+3x^2-2)^5?

1 Answer
Bill K.
May 17, 2016

The derivative is 5(x^4+3x^2-2)^{4} * (4x^3+6x).

Explanation:

The Chain Rule says d/dx(f(g(x))) = f'(g(x)) * g'(x). For the function (x^4+3x^2-2)^5, use f(x)=x^5 and g(x)=x^4+3x^2-2. Then f'(x)=5x^4 and g'(x)=4x^3+6x. Therefore, d/dx((x^4+3x^2-2)^5)=5(x^4+3x^2-2)^{4} * (4x^3+6x).

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