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Popular >

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

Solution

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

Solution

4 x^{3} - 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 4 x^{3} - 2 x

Graph

Popular Examples

derivative of sqrt(x-9)

\frac{d}{d x} (x - 9)

(\partial)/(\partial x)((x-y)/(x+2y))

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

derivative of (sin(1/x)/(x^2))

\frac{d}{d x} (\frac{sin ( \frac{1}{x} )}{x ^{2}})

limit as x approaches-infinity of 9

x \to - \infty lim (9)

integral of (4-3x)^5

\int (4 - 3 x)^{5} d x

Frequently Asked Questions (FAQ)

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