What is the derivative of log_{10}(sqrt(x)) ?

The derivative of log_{10}(sqrt(x)) is 1/(2ln(10)x)

What is the first derivative of log_{10}(sqrt(x)) ?

The first derivative of log_{10}(sqrt(x)) is 1/(2ln(10)x)

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\frac{d}{d x} (lo g_{10} (x))

\frac{1}{2 ln ( 10 ) x}

Solution steps

\frac{d}{d x} (lo g_{10} (x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \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 ( 10 )} \cdot \frac{1}{x} \cdot \frac{1}{2 x}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x} \cdot \frac{1}{2 x} : \frac{1}{2 ln ( 10 ) x}

= \frac{1}{2 ln ( 10 ) x}

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

\int \frac{1}{( a x + b )} d x

e^{x^{2}} + 5 x^{2}

\int \frac{- x ^{2} + x}{x ^{4}} d x

\int \frac{1}{5 + 3 cos ( x )} d x

What is the derivative of log_{10}(sqrt(x)) ?
The derivative of log_{10}(sqrt(x)) is 1/(2ln(10)x)
What is the first derivative of log_{10}(sqrt(x)) ?
The first derivative of log_{10}(sqrt(x)) is 1/(2ln(10)x)