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Popular >

derivative of f(x)=(x+6)/(x+1)

Solution

derivative of

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

Solution

- \frac{5}{( x + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x + 1 ) - 1 \cdot ( x + 6 )}{( x + 1 ) ^{2}} : - \frac{5}{( x + 1 ) ^{2}}

= - \frac{5}{( x + 1 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x+6)/(x+1) ?
The derivative of f(x)=(x+6)/(x+1) is -5/((x+1)^2)
What is the first derivative of f(x)=(x+6)/(x+1) ?
The first derivative of f(x)=(x+6)/(x+1) is -5/((x+1)^2)