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Popular >

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

Solution

derivative of

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

Solution

\frac{1}{2 X}

Solution steps

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

Apply the chain rule:

\frac{1}{X ^{\frac{1}{2}}} \frac{d}{d X} (X^{\frac{1}{2}})

= \frac{1}{X ^{\frac{1}{2}}} \frac{d}{d X} (X^{\frac{1}{2}})

\frac{d}{d X} (X^{\frac{1}{2}}) = \frac{1}{2 X ^{\frac{1}{2}}}

= \frac{1}{X ^{\frac{1}{2}}} \cdot \frac{1}{2 X ^{\frac{1}{2}}}

Simplify

\frac{1}{X ^{\frac{1}{2}}} \cdot \frac{1}{2 X ^{\frac{1}{2}}} : \frac{1}{2 X}

= \frac{1}{2 X}

Graph

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Frequently Asked Questions (FAQ)

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