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Popular >

derivative of (2x^3+8/x)

Solution

\frac{d}{d x} (\frac{2 x ^{3} + 8}{x})

Solution

\frac{4 x ^{3} - 8}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{3} + 8}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 x ^{3} + 8 ) x - \frac{d x}{d x} ( 2 x ^{3} + 8 )}{x ^{2}}

\frac{d}{d x} (2 x^{3} + 8) = 6 x^{2}

\frac{d x}{d x} = 1

= \frac{6 x ^{2} x - 1 \cdot ( 2 x ^{3} + 8 )}{x ^{2}}

Simplify

\frac{6 x ^{2} x - 1 \cdot ( 2 x ^{3} + 8 )}{x ^{2}} : \frac{4 x ^{3} - 8}{x ^{2}}

= \frac{4 x ^{3} - 8}{x ^{2}}

Popular Examples

derivative of 8xcos(x^2)

\frac{d}{d x} (8 x cos (x^{2}))

limit as x approaches 8 of {f(7)g(-7)}

x \to 8 lim ({f (7) g (- 7)})

integral of (4x^2+8)/(2x^2+1)

\int \frac{4 x ^{2} + 8}{2 x ^{2} + 1} d x

integral of 1/(xsqrt(25x^2-4))

\int \frac{1}{x 25 x ^{2} - 4} d x

integral of (e^y)/(1-e^y)

\int \frac{e ^{y}}{1 - e ^{y}} d y

Frequently Asked Questions (FAQ)

What is the derivative of (2x^3+8/x) ?
The derivative of (2x^3+8/x) is (4x^3-8)/(x^2)
What is the first derivative of (2x^3+8/x) ?
The first derivative of (2x^3+8/x) is (4x^3-8)/(x^2)