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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

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

\int \frac{2}{1 + x ^{4}} d x

\frac{1}{6 x}

\int e^{t y} (4 y + 1) d y

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