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Popular >

derivative of ln(x^3-1)

Solution

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

Solution

\frac{3 x ^{2}}{x ^{3} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x ^{3} - 1} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} - 1} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} - 1}

= \frac{3 x ^{2}}{x ^{3} - 1}

Popular Examples

integral from-4 to 2 of (12-x-x^2)-(x+4)

\int_{- 4}^{2} (12 - x - x^{2}) - (x + 4) d x

(\partial)/(\partial x)(x^5+7x^5y)

\frac{\partial}{\partial x} (x^{5} + 7 x^{5} y)

limit as x approaches-4 of (x^2+3)/(x-1)

x \to - 4 lim (\frac{x ^{2} + 3}{x - 1})

e^yy^'+t/(y+1)= 2/(y+1)

e^{y} y^{^{'}} + \frac{t}{y + 1} = \frac{2}{y + 1}

limit as x approaches infinity of 1/(6^{x+1)}

x \to \infty lim (\frac{1}{6 ^{x + 1}})

Frequently Asked Questions (FAQ)

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