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

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

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

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

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

= \frac{1}{ln ( 2 )} \cdot \frac{1}{3 x ^{2}} \cdot 6 x

Simplify

\frac{1}{ln ( 2 )} \cdot \frac{1}{3 x ^{2}} \cdot 6 x : \frac{2}{ln ( 2 ) x}

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

\int 33 + 8 x - x^{2} d x

\int 12 cos^{4} (2 x) sin^{3} (2 x) d x

x^{2} - 4 x - 4

9 x sin (x)

\frac{d}{d x} (\frac{2 sin ( x )}{1 + cos ( x )})

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