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

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

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

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

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derivative of

x^{3} (x - 2)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

y = cos^{2} (x)

\frac{\partial}{\partial x} (8 x^{2} + y^{2} - 7 y)

\frac{d}{d y} (4 x^{2} y^{3} + 2)

\int \frac{x ^{2}}{( 8 - x ^{3} ) ^{2}} d x

72 t

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