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Popular >

derivative of f(x)=(3x+2)(4x^2+3)

Solution

derivative of

f (x) = (3 x + 2) (4 x^{2} + 3)

Solution

36 x^{2} + 16 x + 9

Solution steps

\frac{d}{d x} ((3 x + 2) (4 x^{2} + 3))

Apply the Product Rule:

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

f = 3 x + 2, g = 4 x^{2} + 3

= \frac{d}{d x} (3 x + 2) (4 x^{2} + 3) + \frac{d}{d x} (4 x^{2} + 3) (3 x + 2)

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

= 3 (4 x^{2} + 3) + 8 x (3 x + 2)

Simplify

3 (4 x^{2} + 3) + 8 x (3 x + 2) : 36 x^{2} + 16 x + 9

= 36 x^{2} + 16 x + 9

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(3x+2)(4x^2+3) ?
The derivative of f(x)=(3x+2)(4x^2+3) is 36x^2+16x+9
What is the first derivative of f(x)=(3x+2)(4x^2+3) ?
The first derivative of f(x)=(3x+2)(4x^2+3) is 36x^2+16x+9