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Popular >

derivative of f(x)=(x-1)(x^2+2)^3

Solution

derivative of

f (x) = (x - 1) (x^{2} + 2)^{3}

Solution

(x^{2} + 2)^{3} + 6 x (x^{2} + 2)^{2} (x - 1)

Solution steps

\frac{d}{d x} ((x - 1) (x^{2} + 2)^{3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = (x^{2} + 2)^{3}

= \frac{d}{d x} (x - 1) (x^{2} + 2)^{3} + \frac{d}{d x} ((x^{2} + 2)^{3}) (x - 1)

\frac{d}{d x} (x - 1) = 1

\frac{d}{d x} ((x^{2} + 2)^{3}) = 6 x (x^{2} + 2)^{2}

= 1 \cdot (x^{2} + 2)^{3} + 6 x (x^{2} + 2)^{2} (x - 1)

Simplify

= (x^{2} + 2)^{3} + 6 x (x^{2} + 2)^{2} (x - 1)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x-1)(x^2+2)^3 ?
The derivative of f(x)=(x-1)(x^2+2)^3 is (x^2+2)^3+6x(x^2+2)^2(x-1)
What is the first derivative of f(x)=(x-1)(x^2+2)^3 ?
The first derivative of f(x)=(x-1)(x^2+2)^3 is (x^2+2)^3+6x(x^2+2)^2(x-1)