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Popular >

derivative of f(x)=(6x+14)/(x+7)

Solution

derivative of

f (x) = \frac{6 x + 14}{x + 7}

Solution

\frac{28}{( x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x + 14}{x + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x + 14 ) ( x + 7 ) - \frac{d}{d x} ( x + 7 ) ( 6 x + 14 )}{( x + 7 ) ^{2}}

\frac{d}{d x} (6 x + 14) = 6

\frac{d}{d x} (x + 7) = 1

= \frac{6 ( x + 7 ) - 1 \cdot ( 6 x + 14 )}{( x + 7 ) ^{2}}

Simplify

\frac{6 ( x + 7 ) - 1 \cdot ( 6 x + 14 )}{( x + 7 ) ^{2}} : \frac{28}{( x + 7 ) ^{2}}

= \frac{28}{( x + 7 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(6x+14)/(x+7) ?
The derivative of f(x)=(6x+14)/(x+7) is (28)/((x+7)^2)
What is the first derivative of f(x)=(6x+14)/(x+7) ?
The first derivative of f(x)=(6x+14)/(x+7) is (28)/((x+7)^2)