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

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derivative of

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

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

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