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

The derivative of log_{x}(2) is -(ln(2))/(xln^2(x))

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

The first derivative of log_{x}(2) is -(ln(2))/(xln^2(x))

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derivative of

lo g_{x} (2)

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (1) = 0

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

= ln (2) \frac{0 \cdot ln ( x ) - \frac{1}{x} \cdot 1}{( ln ( x ) ) ^{2}}

Simplify

ln (2) \frac{0 \cdot ln ( x ) - \frac{1}{x} \cdot 1}{ln ^{2} ( x )} : - \frac{ln ( 2 )}{x ln ^{2} ( x )}

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

y = \frac{6}{x}, (16, \frac{6}{4})

y = 2 sin (x) cos (x)

\int 2 tan^{2} (x) + tan^{4} (x) d x

\int \frac{x}{3 x + 1} d x

\int \frac{tan ( θ )}{sec ( θ )} d θ

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