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

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

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

The first derivative of (ln(2x+1)^{1/2}) is 1/(ln^{1/2)(2x+1)(2x+1)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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