What is the derivative of (3x-4/((5x+2)^3)) ?

The derivative of (3x-4/((5x+2)^3)) is (6(-5x+11))/((5x+2)^4)

What is the first derivative of (3x-4/((5x+2)^3)) ?

The first derivative of (3x-4/((5x+2)^3)) is (6(-5x+11))/((5x+2)^4)

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\frac{d}{d x} (\frac{3 x - 4}{( 5 x + 2 ) ^{3}})

\frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{3 x - 4}{( 5 x + 2 ) ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - 4 ) ( 5 x + 2 ) ^{3} - \frac{d}{d x} ( ( 5 x + 2 ) ^{3} ) ( 3 x - 4 )}{( ( 5 x + 2 ) ^{3} ) ^{2}}

\frac{d}{d x} (3 x - 4) = 3

\frac{d}{d x} ((5 x + 2)^{3}) = 15 (5 x + 2)^{2}

= \frac{3 ( 5 x + 2 ) ^{3} - 15 ( 5 x + 2 ) ^{2} ( 3 x - 4 )}{( ( 5 x + 2 ) ^{3} ) ^{2}}

Simplify

\frac{3 ( 5 x + 2 ) ^{3} - 15 ( 5 x + 2 ) ^{2} ( 3 x - 4 )}{( ( 5 x + 2 ) ^{3} ) ^{2}} : \frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

= \frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

What is the derivative of (3x-4/((5x+2)^3)) ?
The derivative of (3x-4/((5x+2)^3)) is (6(-5x+11))/((5x+2)^4)
What is the first derivative of (3x-4/((5x+2)^3)) ?
The first derivative of (3x-4/((5x+2)^3)) is (6(-5x+11))/((5x+2)^4)