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

The derivative of (x^3-2/((x-1)^2)) is (-3x^2+x^3+4)/((x-1)^3)

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

The first derivative of (x^3-2/((x-1)^2)) is (-3x^2+x^3+4)/((x-1)^3)

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

\frac{- 3 x ^{2} + x ^{3} + 4}{( x - 1 ) ^{3}}

Solution steps

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

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

Simplify

\frac{3 x ^{2} ( x - 1 ) ^{2} - 2 ( x - 1 ) ( x ^{3} - 2 )}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{- 3 x ^{2} + x ^{3} + 4}{( x - 1 ) ^{3}}

= \frac{- 3 x ^{2} + x ^{3} + 4}{( x - 1 ) ^{3}}

\int \frac{1}{x ln ( x )} d x

\frac{d}{d x} (x y^{^{'}})

y = x^{4} + 7 x^{2} - x, (1, 7)

\int_{0}^{2} 2 sec (\frac{π x}{6}) d x

2^{x}, 1

What is the derivative of (x^3-2/((x-1)^2)) ?
The derivative of (x^3-2/((x-1)^2)) is (-3x^2+x^3+4)/((x-1)^3)
What is the first derivative of (x^3-2/((x-1)^2)) ?
The first derivative of (x^3-2/((x-1)^2)) is (-3x^2+x^3+4)/((x-1)^3)