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Popular >

derivative of f(x)=(2x-x^3)(3x+7)

Solution

derivative of

f (x) = (2 x - x^{3}) (3 x + 7)

Solution

- 12 x^{3} - 21 x^{2} + 12 x + 14

Solution steps

\frac{d}{d x} ((2 x - x^{3}) (3 x + 7))

Apply the Product Rule:

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

f = 2 x - x^{3}, g = 3 x + 7

= \frac{d}{d x} (2 x - x^{3}) (3 x + 7) + \frac{d}{d x} (3 x + 7) (2 x - x^{3})

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

\frac{d}{d x} (3 x + 7) = 3

= (2 - 3 x^{2}) (3 x + 7) + 3 (2 x - x^{3})

Simplify

(2 - 3 x^{2}) (3 x + 7) + 3 (2 x - x^{3}) : - 12 x^{3} - 21 x^{2} + 12 x + 14

= - 12 x^{3} - 21 x^{2} + 12 x + 14

Popular Examples

derivative of 5x^2+1

\frac{d}{d x} (5 x^{2} + 1)

tangent of f(x)=x^2+4/x-10,\at x=8 tangent of

f (x) = x^{2} + \frac{4}{x} - 10, at x = 8

integral from-3 to 3 of (12-x^2)-(x^2-6)

\int_{- 3}^{3} (12 - x^{2}) - (x^{2} - 6) d x

integral from 1 to e of cos(ln(x))

\int_{1}^{e} cos (ln (x)) d x

integral of (6x^3-3x^2+5+7x^{-1})/(x^3)

\int \frac{6 x ^{3} - 3 x ^{2} + 5 + 7 x ^{- 1}}{x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x-x^3)(3x+7) ?
The derivative of f(x)=(2x-x^3)(3x+7) is -12x^3-21x^2+12x+14
What is the first derivative of f(x)=(2x-x^3)(3x+7) ?
The first derivative of f(x)=(2x-x^3)(3x+7) is -12x^3-21x^2+12x+14