What is the derivative of log_{3}(x^2) ?

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

What is the first derivative of log_{3}(x^2) ?

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

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\frac{d}{d x} (lo g_{3} (x^{2}))

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

Solution steps

\frac{d}{d x} (lo g_{3} (x^{2}))

Apply log rule:

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

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

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (x^{2}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{1}{ln ( x ^{3} )})

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