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

The derivative of f(x)= x/((3x-5)^5) is (-5-12x)/((3x-5)^6)

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

The first derivative of f(x)= x/((3x-5)^5) is (-5-12x)/((3x-5)^6)

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derivative of

f (x) = \frac{x}{( 3 x - 5 ) ^{5}}

\frac{- 5 - 12 x}{( 3 x - 5 ) ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( 3 x - 5 ) ^{5} - 15 ( 3 x - 5 ) ^{4} x}{( ( 3 x - 5 ) ^{5} ) ^{2}} : \frac{- 5 - 12 x}{( 3 x - 5 ) ^{6}}

= \frac{- 5 - 12 x}{( 3 x - 5 ) ^{6}}

What is the derivative of f(x)= x/((3x-5)^5) ?
The derivative of f(x)= x/((3x-5)^5) is (-5-12x)/((3x-5)^6)
What is the first derivative of f(x)= x/((3x-5)^5) ?
The first derivative of f(x)= x/((3x-5)^5) is (-5-12x)/((3x-5)^6)