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

The derivative of (x-5)/(x^2+1) is (-x^2+10x+1)/((x^2+1)^2)

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

The first derivative of (x-5)/(x^2+1) is (-x^2+10x+1)/((x^2+1)^2)

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derivative of

\frac{x - 5}{x ^{2} + 1}

\frac{- x ^{2} + 10 x + 1}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x ^{2} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( x - 5 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (x - 5) = 1

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

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

Simplify

\frac{1 \cdot ( x ^{2} + 1 ) - 2 x ( x - 5 )}{( x ^{2} + 1 ) ^{2}} : \frac{- x ^{2} + 10 x + 1}{( x ^{2} + 1 ) ^{2}}

= \frac{- x ^{2} + 10 x + 1}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{24}{x ^{4}})

\frac{d}{d x} (\frac{1}{5 + 3 x})

\frac{d}{d x} (5 x + \frac{7}{t})

\frac{d}{d x} (∣ sec (x) ∣)

\frac{\partial}{\partial y} (ln (x^{2} - y^{2}))

What is the derivative of (x-5)/(x^2+1) ?
The derivative of (x-5)/(x^2+1) is (-x^2+10x+1)/((x^2+1)^2)
What is the first derivative of (x-5)/(x^2+1) ?
The first derivative of (x-5)/(x^2+1) is (-x^2+10x+1)/((x^2+1)^2)