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

The derivative of ln(2x^3-x^2) is (2(3x-1))/(x(2x-1))

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

The first derivative of ln(2x^3-x^2) is (2(3x-1))/(x(2x-1))

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

\frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{3} - x ^{2}} (6 x^{2} - 2 x)

Simplify

\frac{1}{2 x ^{3} - x ^{2}} (6 x^{2} - 2 x) : \frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

= \frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

What is the derivative of ln(2x^3-x^2) ?
The derivative of ln(2x^3-x^2) is (2(3x-1))/(x(2x-1))
What is the first derivative of ln(2x^3-x^2) ?
The first derivative of ln(2x^3-x^2) is (2(3x-1))/(x(2x-1))