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Popular >

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

Solution

derivative of

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

Solution

14 x^{6} - 16 x^{3} - 16

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (2 x^{3} + 4) = 6 x^{2}

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

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

Simplify

6 x^{2} (x^{4} - 4 x) + (4 x^{3} - 4) (2 x^{3} + 4) : 14 x^{6} - 16 x^{3} - 16

= 14 x^{6} - 16 x^{3} - 16

Popular Examples

derivative of 6/(x^3)-6/(x^2)-1/x+350 derivative of

\frac{6}{x ^{3}} - \frac{6}{x ^{2}} - \frac{1}{x} + 350

derivative of x^3+5x

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

derivative of 2x+2xln(x)

\frac{d}{d x} (2 x + 2 x ln (x))

tangent of (4x+4)^{1/3},\at x=2 tangent of

(4 x + 4)^{\frac{1}{3}}, at x = 2

tangent of y=(-6x)/(x^2+1),(-1,3)tangent of

y = \frac{- 6 x}{x ^{2} + 1}, (- 1, 3)

Frequently Asked Questions (FAQ)

What is the derivative of (2x^3+4)(x^4-4x) ?
The derivative of (2x^3+4)(x^4-4x) is 14x^6-16x^3-16
What is the first derivative of (2x^3+4)(x^4-4x) ?
The first derivative of (2x^3+4)(x^4-4x) is 14x^6-16x^3-16