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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{5}{3 x ^{2} - 2} d x

x \to \infty lim (- 5^{x})

- 3

- \frac{2 sin ( 4 x )}{x}

y = 8 cos (6 x), y = 8 - 8 cos (6 x)

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