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Popular >

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

Solution

derivative of

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

Solution

30 x^{2} - 16 x + 15

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 x (5 x - 4) + 5 (2 x^{2} + 3) : 30 x^{2} - 16 x + 15

= 30 x^{2} - 16 x + 15

Popular Examples

derivative of f(x)=(e^x)/x derivative of

f (x) = \frac{e ^{x}}{x}

limit as x approaches-3 of (x^3+8)/(x+2)

x \to - 3 lim (\frac{x ^{3} + 8}{x + 2})

derivative of e^{2-5x}derivative of

e^{2 - 5 x}

limit as x approaches 0 of (3-7x)/(2x)

x \to 0 lim (\frac{3 - 7 x}{2 x})

maclaurin x^2e^{-x}maclaurin

x^{2} e^{- x}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x^2+3)(5x-4) ?
The derivative of f(x)=(2x^2+3)(5x-4) is 30x^2-16x+15
What is the first derivative of f(x)=(2x^2+3)(5x-4) ?
The first derivative of f(x)=(2x^2+3)(5x-4) is 30x^2-16x+15