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Popular >

derivative of f(x)=(1-x)(x^2-7)^2

Solution

derivative of

f (x) = (1 - x) (x^{2} - 7)^{2}

Solution

- 5 x^{4} + 4 x^{3} + 42 x^{2} - 28 x - 49

Solution steps

\frac{d}{d x} ((1 - x) (x^{2} - 7)^{2})

Apply the Product Rule:

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

f = 1 - x, g = (x^{2} - 7)^{2}

= \frac{d}{d x} (1 - x) (x^{2} - 7)^{2} + \frac{d}{d x} ((x^{2} - 7)^{2}) (1 - x)

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

\frac{d}{d x} ((x^{2} - 7)^{2}) = 4 x (x^{2} - 7)

= (- 1) (x^{2} - 7)^{2} + 4 x (x^{2} - 7) (1 - x)

Simplify

(- 1) (x^{2} - 7)^{2} + 4 x (x^{2} - 7) (1 - x) : - 5 x^{4} + 4 x^{3} + 42 x^{2} - 28 x - 49

= - 5 x^{4} + 4 x^{3} + 42 x^{2} - 28 x - 49

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(1-x)(x^2-7)^2 ?
The derivative of f(x)=(1-x)(x^2-7)^2 is -5x^4+4x^3+42x^2-28x-49
What is the first derivative of f(x)=(1-x)(x^2-7)^2 ?
The first derivative of f(x)=(1-x)(x^2-7)^2 is -5x^4+4x^3+42x^2-28x-49