What is the derivative of (x-3/(x^2-5)) ?

The derivative of (x-3/(x^2-5)) is (-x^2+6x-5)/((x^2-5)^2)

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

The first derivative of (x-3/(x^2-5)) is (-x^2+6x-5)/((x^2-5)^2)

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

\frac{- x ^{2} + 6 x - 5}{( x ^{2} - 5 ) ^{2}}

Solution steps

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

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

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

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

= \frac{1 \cdot ( x ^{2} - 5 ) - 2 x ( x - 3 )}{( x ^{2} - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} - 5 ) - 2 x ( x - 3 )}{( x ^{2} - 5 ) ^{2}} : \frac{- x ^{2} + 6 x - 5}{( x ^{2} - 5 ) ^{2}}

= \frac{- x ^{2} + 6 x - 5}{( x ^{2} - 5 ) ^{2}}

\int x^{3} \cdot e^{x^{4} + 5} d x

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

\int_{0}^{\frac{π}{2}} sec^{2} (x) d x

\int \frac{x ^{3} + 27}{x + 3} d x

\int fdf

What is the derivative of (x-3/(x^2-5)) ?
The derivative of (x-3/(x^2-5)) is (-x^2+6x-5)/((x^2-5)^2)
What is the first derivative of (x-3/(x^2-5)) ?
The first derivative of (x-3/(x^2-5)) is (-x^2+6x-5)/((x^2-5)^2)