What is the derivative of x(x-2)^3 ?

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

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

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

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derivative of

x (x - 2)^{3}

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

Solution steps

\frac{d}{d x} (x (x - 2)^{3})

Apply the Product Rule:

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

f = x, g = (x - 2)^{3}

= \frac{d x}{d x} (x - 2)^{3} + \frac{d}{d x} ((x - 2)^{3}) x

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

\frac{d}{d x} ((x - 2)^{3}) = 3 (x - 2)^{2}

= 1 \cdot (x - 2)^{3} + 3 (x - 2)^{2} x

Simplify

= (x - 2)^{3} + 3 x (x - 2)^{2}

f (x) = \frac{x}{3 + x}

\int_{0}^{π} cos (x) cos (n x) d x

(x^{3} + e^{y}) \frac{d y}{d x} = 3 x^{2}

x \to \infty lim (x - 1)

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + y = 0

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