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

The derivative of ((x+1(x^2+1))/(x-2)) is (2x^3-5x^2-4x-3)/((x-2)^2)

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

The first derivative of ((x+1(x^2+1))/(x-2)) is (2x^3-5x^2-4x-3)/((x-2)^2)

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

\frac{2 x ^{3} - 5 x ^{2} - 4 x - 3}{( x - 2 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{( 3 x ^{2} + 2 x + 1 ) ( x - 2 ) - 1 \cdot ( x + 1 ) ( x ^{2} + 1 )}{( x - 2 ) ^{2}} : \frac{2 x ^{3} - 5 x ^{2} - 4 x - 3}{( x - 2 ) ^{2}}

= \frac{2 x ^{3} - 5 x ^{2} - 4 x - 3}{( x - 2 ) ^{2}}

What is the derivative of ((x+1(x^2+1))/(x-2)) ?
The derivative of ((x+1(x^2+1))/(x-2)) is (2x^3-5x^2-4x-3)/((x-2)^2)
What is the first derivative of ((x+1(x^2+1))/(x-2)) ?
The first derivative of ((x+1(x^2+1))/(x-2)) is (2x^3-5x^2-4x-3)/((x-2)^2)