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Popular Calculus >

derivative of (x^3/(x-1))

Solution

\frac{d}{d x} (\frac{x ^{3}}{x - 1})

Solution

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

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{x - 1})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 1) = 1

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

Simplify

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

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

Graph

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\frac{d}{d x} (cos (2 x + π))

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Frequently Asked Questions (FAQ)

What is the derivative of (x^3/(x-1)) ?
The derivative of (x^3/(x-1)) is (2x^3-3x^2)/((x-1)^2)
What is the first derivative of (x^3/(x-1)) ?
The first derivative of (x^3/(x-1)) is (2x^3-3x^2)/((x-1)^2)