What is the derivative of (x^2+2x-23/(x-4)) ?

The derivative of (x^2+2x-23/(x-4)) is (x^2-8x+15)/((x-4)^2)

What is the first derivative of (x^2+2x-23/(x-4)) ?

The first derivative of (x^2+2x-23/(x-4)) is (x^2-8x+15)/((x-4)^2)

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\frac{d}{d x} (\frac{x ^{2} + 2 x - 23}{x - 4})

\frac{x ^{2} - 8 x + 15}{( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 2 x - 23}{x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 2 x - 23 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x ^{2} + 2 x - 23 )}{( x - 4 ) ^{2}}

\frac{d}{d x} (x^{2} + 2 x - 23) = 2 x + 2

\frac{d}{d x} (x - 4) = 1

= \frac{( 2 x + 2 ) ( x - 4 ) - 1 \cdot ( x ^{2} + 2 x - 23 )}{( x - 4 ) ^{2}}

Simplify

\frac{( 2 x + 2 ) ( x - 4 ) - 1 \cdot ( x ^{2} + 2 x - 23 )}{( x - 4 ) ^{2}} : \frac{x ^{2} - 8 x + 15}{( x - 4 ) ^{2}}

= \frac{x ^{2} - 8 x + 15}{( x - 4 ) ^{2}}

y = 9 cos (x)

\frac{x}{x + 2}

\frac{e ^{- s π}}{s ^{2} + 2 s + 2}

\int 7 csc (x) d x

\frac{d}{d x} (2 x - 6)

What is the derivative of (x^2+2x-23/(x-4)) ?
The derivative of (x^2+2x-23/(x-4)) is (x^2-8x+15)/((x-4)^2)
What is the first derivative of (x^2+2x-23/(x-4)) ?
The first derivative of (x^2+2x-23/(x-4)) is (x^2-8x+15)/((x-4)^2)