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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( 5 x - 4 ) ^{3} - 15 ( 5 x - 4 ) ^{2} x}{( ( 5 x - 4 ) ^{3} ) ^{2}}

Simplify

\frac{1 \cdot ( 5 x - 4 ) ^{3} - 15 ( 5 x - 4 ) ^{2} x}{( ( 5 x - 4 ) ^{3} ) ^{2}} : - \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}

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

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