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Popular >

derivative of (3x-10/(7x+13))

Solution

\frac{d}{d x} (\frac{3 x - 10}{7 x + 13})

Solution

\frac{109}{( 7 x + 13 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x - 10}{7 x + 13})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - 10 ) ( 7 x + 13 ) - \frac{d}{d x} ( 7 x + 13 ) ( 3 x - 10 )}{( 7 x + 13 ) ^{2}}

\frac{d}{d x} (3 x - 10) = 3

\frac{d}{d x} (7 x + 13) = 7

= \frac{3 ( 7 x + 13 ) - 7 ( 3 x - 10 )}{( 7 x + 13 ) ^{2}}

Expand

3 (7 x + 13) - 7 (3 x - 10) : 109

= \frac{109}{( 7 x + 13 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (3x-10/(7x+13)) ?
The derivative of (3x-10/(7x+13)) is (109)/((7x+13)^2)
What is the first derivative of (3x-10/(7x+13)) ?
The first derivative of (3x-10/(7x+13)) is (109)/((7x+13)^2)