What is the derivative of (3x+1/(7x+5)) ?

The derivative of (3x+1/(7x+5)) is 8/((7x+5)^2)

What is the first derivative of (3x+1/(7x+5)) ?

The first derivative of (3x+1/(7x+5)) is 8/((7x+5)^2)

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\frac{d}{d x} (\frac{3 x + 1}{7 x + 5})

\frac{8}{( 7 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 1}{7 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 1 ) ( 7 x + 5 ) - \frac{d}{d x} ( 7 x + 5 ) ( 3 x + 1 )}{( 7 x + 5 ) ^{2}}

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

\frac{d}{d x} (7 x + 5) = 7

= \frac{3 ( 7 x + 5 ) - 7 ( 3 x + 1 )}{( 7 x + 5 ) ^{2}}

Expand

3 (7 x + 5) - 7 (3 x + 1) : 8

= \frac{8}{( 7 x + 5 ) ^{2}}

What is the derivative of (3x+1/(7x+5)) ?
The derivative of (3x+1/(7x+5)) is 8/((7x+5)^2)
What is the first derivative of (3x+1/(7x+5)) ?
The first derivative of (3x+1/(7x+5)) is 8/((7x+5)^2)