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

The derivative of (x^3/(x-2)) is (2x^3-6x^2)/((x-2)^2)

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

The first derivative of (x^3/(x-2)) is (2x^3-6x^2)/((x-2)^2)

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

\frac{2 x ^{3} - 6 x ^{2}}{( x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 x ^{3} - 6 x ^{2}}{( x - 2 ) ^{2}}

\int 9 sin^{3} (x) cos^{5} (x) d x

f (x) = e^{x} - 7 x^{6}

\int csc (θ) + 3 d θ

\frac{d y}{d x} + 9 y - 4 e^{- 2 x} = 0

3 1 + 5 x

What is the derivative of (x^3/(x-2)) ?
The derivative of (x^3/(x-2)) is (2x^3-6x^2)/((x-2)^2)
What is the first derivative of (x^3/(x-2)) ?
The first derivative of (x^3/(x-2)) is (2x^3-6x^2)/((x-2)^2)