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Popular >

derivative of (x^3-2/x)

Solution

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

Solution

\frac{2 x ^{3} + 2}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 x ^{3} + 2}{x ^{2}}

Popular Examples

y^'=(y^2-x^2)/(xy)

y^{^{'}} = \frac{y ^{2} - x ^{2}}{x y}

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

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derivative of 3cos(x)derivative of

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Frequently Asked Questions (FAQ)

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