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Popular >

derivative of ((x+2)/((x+1)))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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\int (1 - e^{- x}) d x

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\int 2 sin (x) d x

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x \to 1 lim (- 2 x^{2} + 5 x + 4)

derivative of (x^2/(x^2+y^2))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + y ^{2}})

Frequently Asked Questions (FAQ)

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