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Popular >

derivative of f(x)=(x^3+8)/x

Solution

derivative of

f (x) = \frac{x ^{3} + 8}{x}

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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