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

The derivative of ln(x^3) is 3/x

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

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

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derivative of

ln (x^{3})

\frac{3}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3}{x}

\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

y = x^{2} (x - 1)

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

\int \frac{1}{( x ^{2} + x + 1 )} d x

(- 5 x + 24)^{\frac{3}{2}}

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