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Popular >

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

Solution

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

Solution

- 3 x^{2} + 8 x - 5

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 (x - 1) (2 - x) + (- 1) (x - 1)^{2} : - 3 x^{2} + 8 x - 5

= - 3 x^{2} + 8 x - 5

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Frequently Asked Questions (FAQ)

What is the derivative of (x-1^2(2-x)) ?
The derivative of (x-1^2(2-x)) is -3x^2+8x-5
What is the first derivative of (x-1^2(2-x)) ?
The first derivative of (x-1^2(2-x)) is -3x^2+8x-5