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

The derivative of (ln(x)/(x^{3/2)}) is (2-3ln(x))/(2x^{5/2)}

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

The first derivative of (ln(x)/(x^{3/2)}) is (2-3ln(x))/(2x^{5/2)}

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Simplify

\frac{\frac{1}{x} x ^{\frac{3}{2}} - \frac{3 x ^{\frac{1}{2}}}{2} ln ( x )}{( x ^{\frac{3}{2}} ) ^{2}} : \frac{2 - 3 ln ( x )}{2 x ^{\frac{5}{2}}}

= \frac{2 - 3 ln ( x )}{2 x ^{\frac{5}{2}}}

x \to 0 - lim (3 - \frac{4}{x})

x^{3}, - 1

\int \frac{e ^{2 x}}{5 + e ^{x}} d x

f (x) = ln (x) - \frac{1}{x}

x^{3} (1 - x)^{100} + x^{4} - 5 π

What is the derivative of (ln(x)/(x^{3/2)}) ?
The derivative of (ln(x)/(x^{3/2)}) is (2-3ln(x))/(2x^{5/2)}
What is the first derivative of (ln(x)/(x^{3/2)}) ?
The first derivative of (ln(x)/(x^{3/2)}) is (2-3ln(x))/(2x^{5/2)}