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Popular >

derivative of (q(-q^2+3q-2))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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