What is the derivative of ln(4/(x^3)) ?

The derivative of ln(4/(x^3)) is -3/x

What is the first derivative of ln(4/(x^3)) ?

The first derivative of ln(4/(x^3)) is -3/x

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

- \frac{3}{x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{4}{x ^{3}}) = - \frac{12}{x ^{4}}

= \frac{1}{\frac{4}{x ^{3}}} (- \frac{12}{x ^{4}})

Simplify

\frac{1}{\frac{4}{x ^{3}}} (- \frac{12}{x ^{4}}) : - \frac{3}{x}

= - \frac{3}{x}

\frac{\partial}{\partial x} (\frac{cos ( 2 y )}{e ^{2 x}})

x \to - 3 + lim (f (x))

\frac{8 x ^{2} + 8 x + 4}{x}

\int \frac{tan ^{3} ( x )}{sec ( x )} d x

\int - u^{2} d u

What is the derivative of ln(4/(x^3)) ?
The derivative of ln(4/(x^3)) is -3/x
What is the first derivative of ln(4/(x^3)) ?
The first derivative of ln(4/(x^3)) is -3/x