What is the derivative of (x-5/(x^2-3x+15)) ?

The derivative of (x-5/(x^2-3x+15)) is (-x^2+10x)/((x^2-3x+15)^2)

What is the first derivative of (x-5/(x^2-3x+15)) ?

The first derivative of (x-5/(x^2-3x+15)) is (-x^2+10x)/((x^2-3x+15)^2)

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\frac{d}{d x} (\frac{x - 5}{x ^{2} - 3 x + 15})

\frac{- x ^{2} + 10 x}{( x ^{2} - 3 x + 15 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x ^{2} - 3 x + 15})

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} - 3 x + 15 ) - \frac{d}{d x} ( x ^{2} - 3 x + 15 ) ( x - 5 )}{( x ^{2} - 3 x + 15 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 3 x + 15) = 2 x - 3

= \frac{1 \cdot ( x ^{2} - 3 x + 15 ) - ( 2 x - 3 ) ( x - 5 )}{( x ^{2} - 3 x + 15 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} - 3 x + 15 ) - ( 2 x - 3 ) ( x - 5 )}{( x ^{2} - 3 x + 15 ) ^{2}} : \frac{- x ^{2} + 10 x}{( x ^{2} - 3 x + 15 ) ^{2}}

= \frac{- x ^{2} + 10 x}{( x ^{2} - 3 x + 15 ) ^{2}}

x \to 2 lim (\frac{e ^{x}}{x ^{3}})

n = 0 \sum \infty \frac{1}{4}^{2}

\int - \frac{x}{1 + x ^{4}} d x

y^{^{'}} = \frac{3}{3 y}

\int x^{3} ln (x^{2} + 1) d x

What is the derivative of (x-5/(x^2-3x+15)) ?
The derivative of (x-5/(x^2-3x+15)) is (-x^2+10x)/((x^2-3x+15)^2)
What is the first derivative of (x-5/(x^2-3x+15)) ?
The first derivative of (x-5/(x^2-3x+15)) is (-x^2+10x)/((x^2-3x+15)^2)