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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derivative of

\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}}

x \to 0 lim ((e^{x} + 3 x)^{\frac{1}{x}})

\int cos (n) t d t

(- 3 + 18 x - 45 x^{2}) (x + 4)

\int (\frac{1}{e ^{x}}) d x

\frac{\partial}{\partial x} (\frac{x + y}{y + 1})

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)