What is the derivative of log_{x}(3) ?

The derivative of log_{x}(3) is -(ln(3))/(xln^2(x))

What is the first derivative of log_{x}(3) ?

The first derivative of log_{x}(3) is -(ln(3))/(xln^2(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (lo g_{x} (3))

- \frac{ln ( 3 )}{x ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (lo g_{x} (3))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 3 )}{ln ( x )})

Take the constant out:

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

= ln (3) \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 (3) \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 (3) \frac{0 \cdot ln ( x ) - \frac{1}{x} \cdot 1}{( ln ( x ) ) ^{2}}

Simplify

ln (3) \frac{0 \cdot ln ( x ) - \frac{1}{x} \cdot 1}{ln ^{2} ( x )} : - \frac{ln ( 3 )}{x ln ^{2} ( x )}

= - \frac{ln ( 3 )}{x ln ^{2} ( x )}

(x^{2} - 4) \frac{d y}{d x} + 2 x y = 3 x^{2}

\frac{1}{( s ^{2} + 4 ) ^{2}}

\frac{d}{d t} (5 t^{- 3})

\int_{- 1}^{1} e^{y} - y^{2} + 2 d y

\frac{\partial}{\partial y} (tan (3 x - 2 y + 1))

What is the derivative of log_{x}(3) ?
The derivative of log_{x}(3) is -(ln(3))/(xln^2(x))
What is the first derivative of log_{x}(3) ?
The first derivative of log_{x}(3) is -(ln(3))/(xln^2(x))