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

The derivative of (x+1)^2(2-x)^2 is 4x^3-6x^2-6x+4

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

The first derivative of (x+1)^2(2-x)^2 is 4x^3-6x^2-6x+4

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (cos^{7} (x^{4} y^{9}))

n = 1 \sum \infty (1 + \frac{1}{n})^{- n}

\frac{d}{d x} (sin^{4} (2 x co) s^{4} 3 x)

\int sec^{2} (x) + 3 d x

\frac{7}{s ( s ^{2} + 5 s )}

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