What is the derivative of log_{5}(x^2) ?

The derivative of log_{5}(x^2) is 2/(ln(5)x)

What is the first derivative of log_{5}(x^2) ?

The first derivative of log_{5}(x^2) is 2/(ln(5)x)

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\frac{d}{d x} (lo g_{5} (x^{2}))

\frac{2}{ln ( 5 ) x}

Solution steps

\frac{d}{d x} (lo g_{5} (x^{2}))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \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 ( 5 )} \cdot \frac{1}{x ^{2}} \cdot 2 x

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{2}} \cdot 2 x : \frac{2}{ln ( 5 ) x}

= \frac{2}{ln ( 5 ) x}

\int \frac{4 w - 11}{2 w ^{2} + 7 w - 4} d w

\int \frac{1}{3 x ^{2} + 4 x + 1} d x

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\frac{d}{d x} (- e^{- 3 x})

What is the derivative of log_{5}(x^2) ?
The derivative of log_{5}(x^2) is 2/(ln(5)x)
What is the first derivative of log_{5}(x^2) ?
The first derivative of log_{5}(x^2) is 2/(ln(5)x)