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Popular >

derivative of (2x+3(5x^2-4x))

Solution

\frac{d}{d x} ((2 x + 3) (5 x^{2} - 4 x))

Solution

30 x^{2} + 14 x - 12

Solution steps

\frac{d}{d x} ((2 x + 3) (5 x^{2} - 4 x))

Apply the Product Rule:

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

f = 2 x + 3, g = 5 x^{2} - 4 x

= \frac{d}{d x} (2 x + 3) (5 x^{2} - 4 x) + \frac{d}{d x} (5 x^{2} - 4 x) (2 x + 3)

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

\frac{d}{d x} (5 x^{2} - 4 x) = 10 x - 4

= 2 (5 x^{2} - 4 x) + (10 x - 4) (2 x + 3)

Simplify

2 (5 x^{2} - 4 x) + (10 x - 4) (2 x + 3) : 30 x^{2} + 14 x - 12

= 30 x^{2} + 14 x - 12

Popular Examples

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\int_{0}^{b} e^{\frac{x}{2}} d x

integral of (x^3)/(3x)

\int \frac{x ^{3}}{3 x} d x

limit as x approaches 2 of (f(x))/(g(x))

x \to 2 lim (\frac{f ( x )}{g ( x )})

integral of ((x^2-x+6))/((x^3-3x))

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

tangent of x^2-6 tangent of

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Frequently Asked Questions (FAQ)

What is the derivative of (2x+3(5x^2-4x)) ?
The derivative of (2x+3(5x^2-4x)) is 30x^2+14x-12
What is the first derivative of (2x+3(5x^2-4x)) ?
The first derivative of (2x+3(5x^2-4x)) is 30x^2+14x-12