What is the derivative of y=log_{10}(3x) ?

The derivative of y=log_{10}(3x) is 1/(ln(10)x)

What is the first derivative of y=log_{10}(3x) ?

The first derivative of y=log_{10}(3x) is 1/(ln(10)x)

derivative of

y = lo g_{10} (3 x)

\frac{1}{ln ( 10 ) x}

Solution steps

\frac{d}{d x} (lo g_{10} (3 x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 3 x )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \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 ( 10 )} \cdot \frac{1}{3 x} \cdot 3

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{3 x} \cdot 3 : \frac{1}{ln ( 10 ) x}

= \frac{1}{ln ( 10 ) x}

d er i v a t i v e f (x) = (1 + 2 e^{x}) sin (x)

d er i v a t i v e - 2^{x}

d er i v a t i v e \frac{1}{4} \cdot x^{2} - \frac{( sin ( 2 x ^{2} ) )}{8}

d er i v a t i v e sin^{4} (3 x - 4 x^{2})

d er i v a t i v e - (e^{- x})^{2}

What is the derivative of y=log_{10}(3x) ?
The derivative of y=log_{10}(3x) is 1/(ln(10)x)
What is the first derivative of y=log_{10}(3x) ?
The first derivative of y=log_{10}(3x) is 1/(ln(10)x)