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

The derivative of ((x+1^3)/((x-1)^2)) is ((x+1)^2(x-5))/((x-1)^3)

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

The first derivative of ((x+1^3)/((x-1)^2)) is ((x+1)^2(x-5))/((x-1)^3)

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

\frac{( x + 1 ) ^{2} ( x - 5 )}{( x - 1 ) ^{3}}

Solution steps

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

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

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

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

Simplify

\frac{3 ( x + 1 ) ^{2} ( x - 1 ) ^{2} - 2 ( x - 1 ) ( x + 1 ) ^{3}}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{( x + 1 ) ^{2} ( x - 5 )}{( x - 1 ) ^{3}}

= \frac{( x + 1 ) ^{2} ( x - 5 )}{( x - 1 ) ^{3}}

\int sin^{3} (2 θ) cos (2 θ) d θ

\int (4 sin (x)) d x

\frac{\partial}{\partial x} (2 sin^{2} (x))

\frac{4 x ^{2} + 4 x + 4}{x}

\frac{d}{d x} (\frac{x ^{3} \cdot e ^{x} - ln ( x )}{sec ( x )})

What is the derivative of ((x+1^3)/((x-1)^2)) ?
The derivative of ((x+1^3)/((x-1)^2)) is ((x+1)^2(x-5))/((x-1)^3)
What is the first derivative of ((x+1^3)/((x-1)^2)) ?
The first derivative of ((x+1^3)/((x-1)^2)) is ((x+1)^2(x-5))/((x-1)^3)