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

The derivative of (x^3/((x-1)^2)) is (x^2(x-3))/((x-1)^3)

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int sin (2 x) cos (2 x) tan (2 x) d x

2 sin^{3} (t)

y^{^{''}} - 5 y^{^{'}} + 5 y = 0

\frac{d}{d x} (\frac{3 x + 2}{x ^{2} - 5 x + 3})

\frac{d}{d x} (cos ((8 x^{2} + 9)^{5}))

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