What is the derivative of log_{2}(sqrt(x)) ?

The derivative of log_{2}(sqrt(x)) is 1/(2ln(2)x)

What is the first derivative of log_{2}(sqrt(x)) ?

The first derivative of log_{2}(sqrt(x)) is 1/(2ln(2)x)

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\frac{d}{d x} (lo g_{2} (x))

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

Solution steps

\frac{d}{d x} (lo g_{2} (x))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(e^{- t} sin (t))^{^{'}}

ln (\frac{x}{x ^{2} + 4})

\frac{\partial}{\partial y} (2 (x + y))

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 3 y})

x \to 2 - lim (x + c)

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