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Popular >

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

Solution

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

Solution

- 6 x^{2} + 14 x - 3

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 - x) = - 1

\frac{d}{d x} (2 x^{2} - x) = 4 x - 1

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

Simplify

(- 1) (2 x^{2} - x) + (4 x - 1) (3 - x) : - 6 x^{2} + 14 x - 3

= - 6 x^{2} + 14 x - 3

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Frequently Asked Questions (FAQ)

What is the derivative of (3-x(2x^2-x)) ?
The derivative of (3-x(2x^2-x)) is -6x^2+14x-3
What is the first derivative of (3-x(2x^2-x)) ?
The first derivative of (3-x(2x^2-x)) is -6x^2+14x-3