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

The derivative of (x^3-x^2+1/(x-2)) is (2x^3-7x^2+4x-1)/((x-2)^2)

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

The first derivative of (x^3-x^2+1/(x-2)) is (2x^3-7x^2+4x-1)/((x-2)^2)

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

\frac{2 x ^{3} - 7 x ^{2} + 4 x - 1}{( x - 2 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{( 3 x ^{2} - 2 x ) ( x - 2 ) - 1 \cdot ( x ^{3} - x ^{2} + 1 )}{( x - 2 ) ^{2}} : \frac{2 x ^{3} - 7 x ^{2} + 4 x - 1}{( x - 2 ) ^{2}}

= \frac{2 x ^{3} - 7 x ^{2} + 4 x - 1}{( x - 2 ) ^{2}}

a x^{2}

\int_{- \infty}^{4} r e^{\frac{r}{2}} d r

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

\int - cos (2 θ) d θ

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

What is the derivative of (x^3-x^2+1/(x-2)) ?
The derivative of (x^3-x^2+1/(x-2)) is (2x^3-7x^2+4x-1)/((x-2)^2)
What is the first derivative of (x^3-x^2+1/(x-2)) ?
The first derivative of (x^3-x^2+1/(x-2)) is (2x^3-7x^2+4x-1)/((x-2)^2)