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

The derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)

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

The first derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)

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

- \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

Solution steps

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

Apply the chain rule:

- \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \frac{d}{d x} (\frac{3 x - 4}{5 x + 2})

= - \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \frac{d}{d x} (\frac{3 x - 4}{5 x + 2})

\frac{d}{d x} (\frac{3 x - 4}{5 x + 2}) = \frac{26}{( 5 x + 2 ) ^{2}}

= - \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \cdot \frac{26}{( 5 x + 2 ) ^{2}}

Simplify

- \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \cdot \frac{26}{( 5 x + 2 ) ^{2}} : - \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

= - \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

d er i v a t i v e f (x) = 5 x^{2} cos (x) + 4 x

d er i v a t i v e 3 x + sin (5 x)

f (x) = ln (cos (x))

\frac{\partial}{\partial x} (\frac{7 y - 7 x}{y ^{2} + 2 x ^{2}})

(x^{2} - 2 x - 2 sin (x - 2))^{^{'}}

What is the derivative of ((3x-4/(5x+2))^{-5}) ?
The derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)
What is the first derivative of ((3x-4/(5x+2))^{-5}) ?
The first derivative of ((3x-4/(5x+2))^{-5}) is -(130(5x+2)^4)/((3x-4)^6)