What is the derivative of ln(x^3(2x-5)^4) ?

The derivative of ln(x^3(2x-5)^4) is (-15+14x)/(x(2x-5))

What is the first derivative of ln(x^3(2x-5)^4) ?

The first derivative of ln(x^3(2x-5)^4) is (-15+14x)/(x(2x-5))

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derivative of

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

\frac{- 15 + 14 x}{x ( 2 x - 5 )}

Solution steps

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

Apply the chain rule:

\frac{1}{x ^{3} ( 2 x - 5 ) ^{4}} \frac{d}{d x} (x^{3} (2 x - 5)^{4})

= \frac{1}{x ^{3} ( 2 x - 5 ) ^{4}} \frac{d}{d x} (x^{3} (2 x - 5)^{4})

\frac{d}{d x} (x^{3} (2 x - 5)^{4}) = 3 x^{2} (2 x - 5)^{4} + 8 (2 x - 5)^{3} x^{3}

= \frac{1}{x ^{3} ( 2 x - 5 ) ^{4}} (3 x^{2} (2 x - 5)^{4} + 8 (2 x - 5)^{3} x^{3})

Simplify

\frac{1}{x ^{3} ( 2 x - 5 ) ^{4}} (3 x^{2} (2 x - 5)^{4} + 8 (2 x - 5)^{3} x^{3}) : \frac{- 15 + 14 x}{x ( 2 x - 5 )}

= \frac{- 15 + 14 x}{x ( 2 x - 5 )}

What is the derivative of ln(x^3(2x-5)^4) ?
The derivative of ln(x^3(2x-5)^4) is (-15+14x)/(x(2x-5))
What is the first derivative of ln(x^3(2x-5)^4) ?
The first derivative of ln(x^3(2x-5)^4) is (-15+14x)/(x(2x-5))