What is the derivative of ln(xsqrt(x)) ?

The derivative of ln(xsqrt(x)) is 3/(2x)

What is the first derivative of ln(xsqrt(x)) ?

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

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derivative of

ln (x x)

\frac{3}{2 x}

Solution steps

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

Simplify

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

= \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}{2}

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

Simplify

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

= \frac{3}{2 x}

18 x - 3 x

\frac{d y}{d t} + 4 y = 2 e^{- 3 t}

\int e^{6 x} cos (x) d x

x \to - 3 lim (2 x + 6)

\frac{d}{d x} (x^{52} - \frac{1}{x ^{2}})

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