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

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

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

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

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derivative of

y = \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 cos (x) (2 + 7 sin^{2} (x)) d x

x \to \infty lim (\frac{2 ^{x + 1} + 3 ^{x}}{2 ^{x} + 3 ^{x + 1}})

x \to 0 + lim (- ln (x))

\int \frac{y ^{2} + 1}{y + 1} d y

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + 1})

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