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

The derivative of (x+5/(x^2+x-6)) is (-x^2-10x-11)/((x^2+x-6)^2)

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

The first derivative of (x+5/(x^2+x-6)) is (-x^2-10x-11)/((x^2+x-6)^2)

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

\frac{- x ^{2} - 10 x - 11}{( x ^{2} + x - 6 ) ^{2}}

Solution steps

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

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

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

\frac{d}{d x} (x^{2} + x - 6) = 2 x + 1

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

Simplify

\frac{1 \cdot ( x ^{2} + x - 6 ) - ( 2 x + 1 ) ( x + 5 )}{( x ^{2} + x - 6 ) ^{2}} : \frac{- x ^{2} - 10 x - 11}{( x ^{2} + x - 6 ) ^{2}}

= \frac{- x ^{2} - 10 x - 11}{( x ^{2} + x - 6 ) ^{2}}

f (x) = x^{\frac{1}{5}} + 8

(- 2, 0), (0, - 4)

x \to 3 lim (h (x) - g (x))

\int π^{2 x} d x

\frac{x ( x + 1 ) d y}{d x} + x y = 1

What is the derivative of (x+5/(x^2+x-6)) ?
The derivative of (x+5/(x^2+x-6)) is (-x^2-10x-11)/((x^2+x-6)^2)
What is the first derivative of (x+5/(x^2+x-6)) ?
The first derivative of (x+5/(x^2+x-6)) is (-x^2-10x-11)/((x^2+x-6)^2)