What is the derivative of y=log_{10}(2x) ?

The derivative of y=log_{10}(2x) is 1/(ln(10)x)

What is the first derivative of y=log_{10}(2x) ?

The first derivative of y=log_{10}(2x) is 1/(ln(10)x)

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derivative of

y = lo g_{10} (2 x)

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

Solution steps

\frac{d}{d x} (lo g_{10} (2 x))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 2 x )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (2 x))

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{2 x} \cdot 2

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{2 x} \cdot 2 : \frac{1}{ln ( 10 ) x}

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

sin (y^{2})

y = sin^{2} (x) 0.2 x

y = e^{3} x

(x^{2} + 3 x + 2)^{2} + ln (e) x^{2}

e^{2 x - 1}

What is the derivative of y=log_{10}(2x) ?
The derivative of y=log_{10}(2x) is 1/(ln(10)x)
What is the first derivative of y=log_{10}(2x) ?
The first derivative of y=log_{10}(2x) is 1/(ln(10)x)