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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{7 x y ^{2}}{x ^{2} + y ^{4}})

\int \frac{cos ( x )}{sin ^{2} ( x ) + 2 sin ( x )} d x

\int 2 e^{- \frac{x}{4}} d x

x \to 9 + lim (6)

y^{^{'}} = y - x + 1

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