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

The derivative of f(x)=log_{2}(3x) is 1/(ln(2)x)

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

The first derivative of f(x)=log_{2}(3x) is 1/(ln(2)x)

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derivative of

f (x) = lo g_{2} (3 x)

\frac{1}{ln ( 2 ) x}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{ln ( 2 ) x}

in v erse l a pl a ce \frac{s - 1}{s ^{2} ( s + 3 )}

t \to a lim (t)

t an g e n t x^{2} - 2 x

d er i v a t i v e 7 x^{2} - 8 x + 3

\frac{\partial}{\partial x} (x^{2} y^{2})

What is the derivative of f(x)=log_{2}(3x) ?
The derivative of f(x)=log_{2}(3x) is 1/(ln(2)x)
What is the first derivative of f(x)=log_{2}(3x) ?
The first derivative of f(x)=log_{2}(3x) is 1/(ln(2)x)