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Popular >

derivative of (x+6)/(x+2)

Solution

derivative of

\frac{x + 6}{x + 2}

Solution

- \frac{4}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 6}{x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 6 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x + 6 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x + 6) = 1

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

= \frac{1 \cdot ( x + 2 ) - 1 \cdot ( x + 6 )}{( x + 2 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 2 ) - 1 \cdot ( x + 6 )}{( x + 2 ) ^{2}} : - \frac{4}{( x + 2 ) ^{2}}

= - \frac{4}{( x + 2 ) ^{2}}

Popular Examples

y^'+1/x y=-4y^2

y^{^{'}} + \frac{1}{x} y = - 4 y^{2}

integral from 0 to 1 of (81)/(x^5)

\int_{0}^{1} \frac{81}{x ^{5}} d x

x(dy)/(dx)+y=2x

x \frac{d y}{d x} + y = 2 x

limit as x approaches 0+of 1+x^{(1/x)}

x \to 0 + lim (1 + x^{(\frac{1}{x})})

integral from-2 to-1 of x-1/(x^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of (x+6)/(x+2) ?
The derivative of (x+6)/(x+2) is -4/((x+2)^2)
What is the first derivative of (x+6)/(x+2) ?
The first derivative of (x+6)/(x+2) is -4/((x+2)^2)