What is the derivative of log_{5}(2x-5) ?

The derivative of log_{5}(2x-5) is 2/(ln(5)(2x-5))

What is the first derivative of log_{5}(2x-5) ?

The first derivative of log_{5}(2x-5) is 2/(ln(5)(2x-5))

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\frac{d}{d x} (lo g_{5} (2 x - 5))

\frac{2}{ln ( 5 ) ( 2 x - 5 )}

Solution steps

\frac{d}{d x} (lo g_{5} (2 x - 5))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 2 x - 5 )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (2 x - 5))

Apply the chain rule:

\frac{1}{2 x - 5} \frac{d}{d x} (2 x - 5)

= \frac{1}{2 x - 5} \frac{d}{d x} (2 x - 5)

\frac{d}{d x} (2 x - 5) = 2

= \frac{1}{ln ( 5 )} \cdot \frac{1}{2 x - 5} \cdot 2

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{2 x - 5} \cdot 2 : \frac{2}{ln ( 5 ) ( 2 x - 5 )}

= \frac{2}{ln ( 5 ) ( 2 x - 5 )}

f (x) = \frac{5}{x}, at x = \frac{1}{4}

\int (y - x) d x

x \to - 1 lim (\frac{x ^{2} - 1}{x - 1})

\int \frac{2 v ^{3} - v}{v ^{4} - v ^{2}} d v

x y^{2} \frac{d y}{d x} = y^{3} - x^{2}

What is the derivative of log_{5}(2x-5) ?
The derivative of log_{5}(2x-5) is 2/(ln(5)(2x-5))
What is the first derivative of log_{5}(2x-5) ?
The first derivative of log_{5}(2x-5) is 2/(ln(5)(2x-5))