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Popular >

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

Solution

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

Solution

\frac{3}{( 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{3}{( x + 2 ) ^{2}}

= \frac{3}{( x + 2 ) ^{2}}

Popular Examples

(\partial)/(\partial x)(x/4+sqrt(y))

\frac{\partial}{\partial x} (\frac{x}{4} + y)

(\partial)/(\partial x)(b)

\frac{\partial}{\partial x} (b)

derivative of xl

\frac{d}{d x} (x l)

taylor 1/(sqrt(1-x^2))taylor

\frac{1}{1 - x ^{2}}

limit as x approaches infinity of 2x

x \to \infty lim (2 x)

Frequently Asked Questions (FAQ)

What is the derivative of (x-1/(x+2)) ?
The derivative of (x-1/(x+2)) is 3/((x+2)^2)
What is the first derivative of (x-1/(x+2)) ?
The first derivative of (x-1/(x+2)) is 3/((x+2)^2)