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Popular >

derivative of f(x)=(3-x)/(x+1)

Solution

derivative of

f (x) = \frac{3 - x}{x + 1}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 1 ) ( x + 1 ) - 1 \cdot ( 3 - x )}{( x + 1 ) ^{2}} : - \frac{4}{( x + 1 ) ^{2}}

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

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\frac{d}{d x} (e^{- x} cos (5 x))

slope of (8 1/7 ,9),(4,3.2)slope

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limit as x approaches 0 of ((3e^{-x}-3))/(x^2-2x)

x \to 0 lim (\frac{( 3 e ^{- x} - 3 )}{x ^{2} - 2 x})

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x \to - 35 lim (34 + x)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(3-x)/(x+1) ?
The derivative of f(x)=(3-x)/(x+1) is -4/((x+1)^2)
What is the first derivative of f(x)=(3-x)/(x+1) ?
The first derivative of f(x)=(3-x)/(x+1) is -4/((x+1)^2)