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Popular >

derivative of (ln(x)^{1/2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (-x^2-1/((x^2-1)^2))

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

integral of e^{-t}*(-t^2+t-1)

\int e^{- t} \cdot (- t^{2} + t - 1) d t

integral from 0 to 4 of (2+xsqrt(x))

\int_{0}^{4} (2 + x x) d x

integral of 2(1-x)

\int 2 (1 - x) d x

integral of 2/3 x^{3/2}*1/x

\int \frac{2}{3} x^{\frac{3}{2}} \cdot \frac{1}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (ln(x)^{1/2}) ?
The derivative of (ln(x)^{1/2}) is 1/(2xln^{1/2)(x)}
What is the first derivative of (ln(x)^{1/2}) ?
The first derivative of (ln(x)^{1/2}) is 1/(2xln^{1/2)(x)}