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Popular >

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

Solution

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

Solution

- 3 x^{2} + 3

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - 3 x^{2} + 3

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(dy)/(dx)=-((y^2))/(1+y^2)*e^{-x}

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Frequently Asked Questions (FAQ)

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