What is the derivative of f(x)= x/((5x-9)^5) ?

The derivative of f(x)= x/((5x-9)^5) is (-9-20x)/((5x-9)^6)

What is the first derivative of f(x)= x/((5x-9)^5) ?

The first derivative of f(x)= x/((5x-9)^5) is (-9-20x)/((5x-9)^6)

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derivative of

f (x) = \frac{x}{( 5 x - 9 ) ^{5}}

\frac{- 9 - 20 x}{( 5 x - 9 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{x}{( 5 x - 9 ) ^{5}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 5 x - 9 ) ^{5} - \frac{d}{d x} ( ( 5 x - 9 ) ^{5} ) x}{( ( 5 x - 9 ) ^{5} ) ^{2}}

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

\frac{d}{d x} ((5 x - 9)^{5}) = 25 (5 x - 9)^{4}

= \frac{1 \cdot ( 5 x - 9 ) ^{5} - 25 ( 5 x - 9 ) ^{4} x}{( ( 5 x - 9 ) ^{5} ) ^{2}}

Simplify

\frac{1 \cdot ( 5 x - 9 ) ^{5} - 25 ( 5 x - 9 ) ^{4} x}{( ( 5 x - 9 ) ^{5} ) ^{2}} : \frac{- 9 - 20 x}{( 5 x - 9 ) ^{6}}

= \frac{- 9 - 20 x}{( 5 x - 9 ) ^{6}}

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What is the derivative of f(x)= x/((5x-9)^5) ?
The derivative of f(x)= x/((5x-9)^5) is (-9-20x)/((5x-9)^6)
What is the first derivative of f(x)= x/((5x-9)^5) ?
The first derivative of f(x)= x/((5x-9)^5) is (-9-20x)/((5x-9)^6)