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Popular >

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

Solution

derivative of

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

Solution

18 x^{2} + 6 x + 4

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (3 x^{2} + 2) = 6 x

= 2 (3 x^{2} + 2) + 6 x (2 x + 1)

Simplify

2 (3 x^{2} + 2) + 6 x (2 x + 1) : 18 x^{2} + 6 x + 4

= 18 x^{2} + 6 x + 4

Popular Examples

integral of (e^x)/(sqrt(e^{2x)-1)}

\int \frac{e ^{x}}{e ^{2 x} - 1} d x

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\int_{0}^{4} \frac{3}{x ^{2}} d x

area y=10-x^2,y=4 area

y = 10 - x^{2}, y = 4

(d^2)/(dx^2)(5e^x)

\frac{d ^{2}}{d x ^{2}} (5 e^{x})

tangent of f(x)=5x^2-4x+3 tangent of

f (x) = 5 x^{2} - 4 x + 3

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x+1)(3x^2+2) ?
The derivative of f(x)=(2x+1)(3x^2+2) is 18x^2+6x+4
What is the first derivative of f(x)=(2x+1)(3x^2+2) ?
The first derivative of f(x)=(2x+1)(3x^2+2) is 18x^2+6x+4