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

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

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

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

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2}) = 4 x

= \frac{1}{ln ( 5 )} \cdot \frac{1}{2 x ^{2}} \cdot 4 x

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{2 x ^{2}} \cdot 4 x : \frac{2}{ln ( 5 ) x}

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

\frac{d}{d y} (e^{y} cos (y))

\int tan^{2} (x) sec^{6} (x) d x

\int x (x^{2} + 1)^{100} d x

\frac{x ^{2} - 10 x + 65}{x - 8}

n = 0 \sum \infty \frac{1}{( 2 n - 1 ) ^{2}}

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