What is the derivative of f(x)=x(2-x)^2 ?

The derivative of f(x)=x(2-x)^2 is 3x^2-8x+4

What is the first derivative of f(x)=x(2-x)^2 ?

The first derivative of f(x)=x(2-x)^2 is 3x^2-8x+4

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derivative of

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

3 x^{2} - 8 x + 4

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot (2 - x)^{2} + (- 2 (2 - x)) x : 3 x^{2} - 8 x + 4

= 3 x^{2} - 8 x + 4

\int t^{2} e^{5 t} d t

\frac{d}{d x} (e^{2 x^{2} - 5 x})

\frac{d ^{2}}{d x ^{2}} (4 x^{2})

\int_{0}^{2} \frac{x ^{2} + 2}{x + 1} d x

\int - \frac{2 x}{1 - x ^{2}} d x

What is the derivative of f(x)=x(2-x)^2 ?
The derivative of f(x)=x(2-x)^2 is 3x^2-8x+4
What is the first derivative of f(x)=x(2-x)^2 ?
The first derivative of f(x)=x(2-x)^2 is 3x^2-8x+4