What is the derivative of ln(x^{3/2}) ?

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

What is the first derivative of ln(x^{3/2}) ?

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

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derivative of

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

\frac{3}{2 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3}{2 x}

\frac{10}{s ( s + 2 )}

f (x) = 4 x^{2} + 5 x + 1, (0, 1)

y = \frac{4 - 3 x}{3 x ^{2} + x}

630 - 4.9 t^{2}

x \to \frac{π}{2} lim (8 sec (x))

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