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Popular >

derivative of ((ln(x))/(sqrt(x)))

Solution

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

Solution

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

Solution steps

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

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{d}{d x} ( x ) ln ( x )}{( x ) ^{2}}

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to 3/4 of sin^2(pix)

\int_{0}^{\frac{3}{4}} sin^{2} (π x) d x

(\partial)/(\partial y)(2xy-e^{2y})

\frac{\partial}{\partial y} (2 x y - e^{2 y})

(\partial)/(\partial x)((e^x+e^y)^9)

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{9})

derivative of f(x)=3e^{4x}derivative of

f (x) = 3 e^{4 x}

y^{''}+25y=25sec^2(5x)

y^{^{''}} + 25 y = 25 sec^{2} (5 x)

Frequently Asked Questions (FAQ)

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