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Popular >

derivative of (3x^2+2(2x-3))

Solution

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

Solution

18 x^{2} - 18 x + 4

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (7x^2)/((9+x^2)^2)

\int \frac{7 x ^{2}}{( 9 + x ^{2} ) ^{2}} d x

integral from 0 to 1 of 16sin^4(x)

\int_{0}^{1} 16 sin^{4} (x) d x

limit as x approaches 3 of (x-3)/((x-3))

x \to 3 lim (\frac{x - 3}{( x - 3 )})

y^{''}-2y^'+10y=0

y^{^{''}} - 2 y^{^{'}} + 10 y = 0

derivative of e^{4/x}

\frac{d}{d x} (e^{\frac{4}{x}})

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2+2(2x-3)) ?
The derivative of (3x^2+2(2x-3)) is 18x^2-18x+4
What is the first derivative of (3x^2+2(2x-3)) ?
The first derivative of (3x^2+2(2x-3)) is 18x^2-18x+4