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Popular >

derivative of (1-x^2\times (x-1)^2)

Solution

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

Solution

- 4 x^{3} + 6 x^{2} - 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- 2 x) (x - 1)^{2} + 2 (x - 1) (1 - x^{2}) : - 4 x^{3} + 6 x^{2} - 2

= - 4 x^{3} + 6 x^{2} - 2

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Frequently Asked Questions (FAQ)

What is the derivative of (1-x^2\times (x-1)^2) ?
The derivative of (1-x^2\times (x-1)^2) is -4x^3+6x^2-2
What is the first derivative of (1-x^2\times (x-1)^2) ?
The first derivative of (1-x^2\times (x-1)^2) is -4x^3+6x^2-2