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Popular >

derivative of (x-4)/(x+2)

Solution

derivative of

\frac{x - 4}{x + 2}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 4) = 1

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

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

Simplify

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

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

Popular Examples

integral of (2x+1)/((x-1)(x+4)^2)

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

integral of 1/(sqrt(x-1)-\sqrt{x)}

\int \frac{1}{x - 1 - x} d x

integral of (-2y)/x

\int \frac{- 2 y}{x} d x

limit as x approaches 5+of (-3)/(x^2-25)

x \to 5 + lim (\frac{- 3}{x ^{2} - 25})

(1+x^2)y^'=x(1-y)

(1 + x^{2}) y^{^{'}} = x (1 - y)

Frequently Asked Questions (FAQ)

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