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Popular >

derivative of f(x)=(x^2+3x)(x-1)

Solution

derivative of

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

Solution

3 x^{2} + 4 x - 3

Solution steps

\frac{d}{d x} ((x^{2} + 3 x) (x - 1))

Apply the Product Rule:

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

f = x^{2} + 3 x, g = x - 1

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2+3x)(x-1) ?
The derivative of f(x)=(x^2+3x)(x-1) is 3x^2+4x-3
What is the first derivative of f(x)=(x^2+3x)(x-1) ?
The first derivative of f(x)=(x^2+3x)(x-1) is 3x^2+4x-3