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Popular >

derivative of x^2(2x^2-3x)

Solution

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

Solution

8 x^{3} - 9 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (2 x^{2} - 3 x) = 4 x - 3

= 2 x (2 x^{2} - 3 x) + (4 x - 3) x^{2}

Simplify

2 x (2 x^{2} - 3 x) + (4 x - 3) x^{2} : 8 x^{3} - 9 x^{2}

= 8 x^{3} - 9 x^{2}

Popular Examples

derivative of 3x^2

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

tangent of f(x)=x-5sin(x),\at x= pi/2 tangent of

f (x) = x - 5 sin (x), at x = \frac{π}{2}

limit as x approaches-7+of (x+6)/(x+7)

x \to - 7 + lim (\frac{x + 6}{x + 7})

integral of (12)/(sqrt(x))

\int \frac{12}{x} d x

limit as x approaches 0 of | 1/x |

x \to 0 lim (\frac{1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of x^2(2x^2-3x) ?
The derivative of x^2(2x^2-3x) is 8x^3-9x^2
What is the first derivative of x^2(2x^2-3x) ?
The first derivative of x^2(2x^2-3x) is 8x^3-9x^2