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Popular >

derivative of (x+3/(x+2))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 3) = 1

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

= \frac{1 \cdot ( x + 2 ) - 1 \cdot ( x + 3 )}{( x + 2 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 2 ) - 1 \cdot ( x + 3 )}{( x + 2 ) ^{2}} : - \frac{1}{( x + 2 ) ^{2}}

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

Popular Examples

derivative of 4/(4-10x)

\frac{d}{d x} (\frac{4}{4 - 10 x})

derivative of (x^2-2/x)

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

tangent of x^2+2xy-y^2+x=5,(3,7)tangent of

x^{2} + 2 x y - y^{2} + x = 5, (3, 7)

\frac{d}{d t} (t ln (t))

limit as x approaches 0+of x/(ln(x))

x \to 0 + lim (\frac{x}{ln ( x )})

Frequently Asked Questions (FAQ)

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