What is the derivative of x/((3x-8^8)) ?

The derivative of x/((3x-8^8)) is (-8-21x)/((3x-8)^9)

What is the first derivative of x/((3x-8^8)) ?

The first derivative of x/((3x-8^8)) is (-8-21x)/((3x-8)^9)

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\frac{d}{d x} (\frac{x}{( 3 x - 8 ) ^{8}})

\frac{- 8 - 21 x}{( 3 x - 8 ) ^{9}}

Solution steps

\frac{d}{d x} (\frac{x}{( 3 x - 8 ) ^{8}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 3 x - 8 ) ^{8} - \frac{d}{d x} ( ( 3 x - 8 ) ^{8} ) x}{( ( 3 x - 8 ) ^{8} ) ^{2}}

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

\frac{d}{d x} ((3 x - 8)^{8}) = 24 (3 x - 8)^{7}

= \frac{1 \cdot ( 3 x - 8 ) ^{8} - 24 ( 3 x - 8 ) ^{7} x}{( ( 3 x - 8 ) ^{8} ) ^{2}}

Simplify

\frac{1 \cdot ( 3 x - 8 ) ^{8} - 24 ( 3 x - 8 ) ^{7} x}{( ( 3 x - 8 ) ^{8} ) ^{2}} : \frac{- 8 - 21 x}{( 3 x - 8 ) ^{9}}

= \frac{- 8 - 21 x}{( 3 x - 8 ) ^{9}}

What is the derivative of x/((3x-8^8)) ?
The derivative of x/((3x-8^8)) is (-8-21x)/((3x-8)^9)
What is the first derivative of x/((3x-8^8)) ?
The first derivative of x/((3x-8^8)) is (-8-21x)/((3x-8)^9)