What is the derivative of (x-7/(x+2)) ?

The derivative of (x-7/(x+2)) is 9/((x+2)^2)

What is the first derivative of (x-7/(x+2)) ?

The first derivative of (x-7/(x+2)) is 9/((x+2)^2)

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\frac{d}{d x} (\frac{x - 7}{x + 2})

\frac{9}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 7}{x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 7 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x - 7 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x - 7) = 1

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

= \frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 7 )}{( x + 2 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 7 )}{( x + 2 ) ^{2}} : \frac{9}{( x + 2 ) ^{2}}

= \frac{9}{( x + 2 ) ^{2}}

\int \frac{1}{12 - 4 x - x ^{2}} d x

x^{2} - 2, e^{x}, [- 1, 1]

\frac{( 4 x ^{3} )}{( 2 - 3 x ) ^{5}}

\int + sin^{3} (θ) cos^{4} (θ) d θ

\frac{x + 9}{x ^{3} + x - 2}

What is the derivative of (x-7/(x+2)) ?
The derivative of (x-7/(x+2)) is 9/((x+2)^2)
What is the first derivative of (x-7/(x+2)) ?
The first derivative of (x-7/(x+2)) is 9/((x+2)^2)