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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

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

\int \frac{1}{( 2 x + 3 y ) ^{2}} d x

\int sin^{2} (3 x co) s^{2} 3 x d x

\frac{d y}{d x} = e^{y + x}

\frac{d}{d v} (u sin (v))

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