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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

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

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

Simplify

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

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

3 y^{^{''}} + 13 y^{^{'}} + 4 = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{d}{d x} (3 (7 - 3 x^{3})^{3})

- (1 + y^{2})^{\frac{1}{2}} d x + 4 x y d y = 0

\frac{d}{d x} (1 + csc (x))

x \to - \infty lim (- x e^{x})

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