What is the derivative of (-8x+2/(3x+5)) ?

The derivative of (-8x+2/(3x+5)) is -(46)/((3x+5)^2)

What is the first derivative of (-8x+2/(3x+5)) ?

The first derivative of (-8x+2/(3x+5)) is -(46)/((3x+5)^2)

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\frac{d}{d x} (\frac{- 8 x + 2}{3 x + 5})

- \frac{46}{( 3 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 8 x + 2}{3 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( - 8 x + 2 ) ( 3 x + 5 ) - \frac{d}{d x} ( 3 x + 5 ) ( - 8 x + 2 )}{( 3 x + 5 ) ^{2}}

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

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

= \frac{( - 8 ) ( 3 x + 5 ) - 3 ( - 8 x + 2 )}{( 3 x + 5 ) ^{2}}

Simplify

\frac{( - 8 ) ( 3 x + 5 ) - 3 ( - 8 x + 2 )}{( 3 x + 5 ) ^{2}} : - \frac{46}{( 3 x + 5 ) ^{2}}

= - \frac{46}{( 3 x + 5 ) ^{2}}

x \to - 13 lim (- 12)

f (x) = \frac{x ^{3} + 2}{3}

\frac{4}{x}, at x = 3

\frac{s ^{2} + 1}{s + 5}

\int \frac{10800}{9 q ^{2} + 675} d q

What is the derivative of (-8x+2/(3x+5)) ?
The derivative of (-8x+2/(3x+5)) is -(46)/((3x+5)^2)
What is the first derivative of (-8x+2/(3x+5)) ?
The first derivative of (-8x+2/(3x+5)) is -(46)/((3x+5)^2)