What is the derivative of ln(x^4sqrt(8-6x)) ?

The derivative of ln(x^4sqrt(8-6x)) is (-27x+32)/(2x(-3x+4))

What is the first derivative of ln(x^4sqrt(8-6x)) ?

The first derivative of ln(x^4sqrt(8-6x)) is (-27x+32)/(2x(-3x+4))

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\frac{d}{d x} (ln (x^{4} 8 - 6 x))

\frac{- 27 x + 32}{2 x ( - 3 x + 4 )}

Solution steps

\frac{d}{d x} (ln (x^{4} 8 - 6 x))

Apply the chain rule:

\frac{1}{x ^{4} 8 - 6 x} \frac{d}{d x} (x^{4} 8 - 6 x)

= \frac{1}{x ^{4} 8 - 6 x} \frac{d}{d x} (x^{4} 8 - 6 x)

\frac{d}{d x} (x^{4} 8 - 6 x) = \frac{- 27 x ^{4} + 32 x ^{3}}{8 - 6 x}

= \frac{1}{x ^{4} 8 - 6 x} \cdot \frac{- 27 x ^{4} + 32 x ^{3}}{8 - 6 x}

Simplify

\frac{1}{x ^{4} 8 - 6 x} \cdot \frac{- 27 x ^{4} + 32 x ^{3}}{8 - 6 x} : \frac{- 27 x + 32}{2 x ( - 3 x + 4 )}

= \frac{- 27 x + 32}{2 x ( - 3 x + 4 )}

What is the derivative of ln(x^4sqrt(8-6x)) ?
The derivative of ln(x^4sqrt(8-6x)) is (-27x+32)/(2x(-3x+4))
What is the first derivative of ln(x^4sqrt(8-6x)) ?
The first derivative of ln(x^4sqrt(8-6x)) is (-27x+32)/(2x(-3x+4))