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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{4}{4 + e ^{x}} d x

\frac{d}{d t} ((\frac{2 t + 5}{t ^{2} + 1})^{4})

\frac{\partial}{\partial u} (\frac{1}{u ^{2} + v ^{2}})

\frac{d}{d I} (\frac{100 I}{I ^{2} + I + 4})

\int \frac{y ^{6}}{2 y ^{7} + 2} d y

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