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Popular >

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

Solution

derivative of

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

Solution

9 x^{2} + 2 x - 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 (x^{2} - 2) + 2 x (3 x + 1) : 9 x^{2} + 2 x - 6

= 9 x^{2} + 2 x - 6

Popular Examples

integral of 4/(sqrt(x^2-4x+13))

\int \frac{4}{x ^{2} - 4 x + 13} d x

integral from 0 to 5 of 1/(x-3)

\int_{0}^{5} \frac{1}{x - 3} d x

limit as θ approaches 0 of θ/(sin^2(θ))

θ \to 0 lim (\frac{θ}{sin ^{2} ( θ )})

limit as x approaches 2 of x^2-7x+12

x \to 2 lim (x^{2} - 7 x + 12)

inverse oflaplace 1/((s^3+s^2+s))inverse laplace

\frac{1}{( s ^{3} + s ^{2} + s )}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(3x+1)(x^2-2) ?
The derivative of f(x)=(3x+1)(x^2-2) is 9x^2+2x-6
What is the first derivative of f(x)=(3x+1)(x^2-2) ?
The first derivative of f(x)=(3x+1)(x^2-2) is 9x^2+2x-6