What is the derivative of sqrt(ln(-5x+2x^{-2)}) ?

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

What is the first derivative of sqrt(ln(-5x+2x^{-2)}) ?

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

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 ln ( - 5 x + 2 x ^{- 2} )} \frac{d}{d x} (ln (- 5 x + 2 x^{- 2}))

= \frac{1}{2 ln ( - 5 x + 2 x ^{- 2} )} \frac{d}{d x} (ln (- 5 x + 2 x^{- 2}))

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

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

Simplify

\frac{1}{2 ln ( - 5 x + 2 x ^{- 2} )} \cdot \frac{- 5 x ^{3} - 4}{x ( - 5 x ^{3} + 2 )} : \frac{- 5 x ^{3} - 4}{2 x ( - 5 x ^{3} + 2 ) ln ( - 5 x ^{3} + 2 ) - 2 ln ( x )}

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

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