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

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

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

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

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

\frac{3}{2 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}) = \frac{3 x}{2}

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

Simplify

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

= \frac{3}{2 x}

\frac{d}{d x} ((\frac{1}{2} x)^{5})

x \to \infty lim ((x)^{\frac{l n ( 2 )}{1 + l n ( x )}})

f (x) = \frac{100}{( 1 + 5 x ) ^{3}}

\int x^{3} + sin (x) + cos (x) d x

\int e^{8 x} sin (9 x) d x

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