What is the derivative of log_{10}(2x-3) ?

The derivative of log_{10}(2x-3) is 2/(ln(10)(2x-3))

What is the first derivative of log_{10}(2x-3) ?

The first derivative of log_{10}(2x-3) is 2/(ln(10)(2x-3))

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\frac{d}{d x} (lo g_{10} (2 x - 3))

\frac{2}{ln ( 10 ) ( 2 x - 3 )}

Solution steps

\frac{d}{d x} (lo g_{10} (2 x - 3))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 2 x - 3 )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (2 x - 3))

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{2 x - 3} \cdot 2

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{2 x - 3} \cdot 2 : \frac{2}{ln ( 10 ) ( 2 x - 3 )}

= \frac{2}{ln ( 10 ) ( 2 x - 3 )}

\int \frac{x ^{2} + 12 x - 4}{x ^{3} - 4 x} d x

\frac{\partial}{\partial x} (4 x ln (y) + y ln (z) - 4 x)

\int \frac{x ^{2}}{x - 10} d x

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

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

What is the derivative of log_{10}(2x-3) ?
The derivative of log_{10}(2x-3) is 2/(ln(10)(2x-3))
What is the first derivative of log_{10}(2x-3) ?
The first derivative of log_{10}(2x-3) is 2/(ln(10)(2x-3))