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Popular >

derivative of ln(2x^3-x^2)

Solution

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

Solution

\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 )}

Popular Examples

derivative of sqrt(5x^3)

\frac{d}{d x} (5 x^{3})

derivative of 4/(3x^3)

\frac{d}{d x} (\frac{4}{3 x ^{3}})

integral of x^3sqrt(x^2-5)

\int x^{3} x^{2} - 5 d x

(dy)/(dx)-3/x y=x^3

\frac{d y}{d x} - \frac{3}{x} y = x^{3}

sum from k=1 to infinity of 0

k = 1 \sum \infty 0

Frequently Asked Questions (FAQ)

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))