What is the derivative of log_{10}(x-1) ?

The derivative of log_{10}(x-1) is 1/(ln(10)(x-1))

What is the first derivative of log_{10}(x-1) ?

The first derivative of log_{10}(x-1) is 1/(ln(10)(x-1))

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derivative of

lo g_{10} (x - 1)

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

Solution steps

\frac{d}{d x} (lo g_{10} (x - 1))

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

sin (x^{2} + 5)

\frac{d}{d s} (3 s^{2})

y = \frac{( x ^{5} + x ^{2} )}{( x ^{3} + 1 )}

\frac{d}{d r} (5 (r - 2 \cdot p))

\frac{d}{d t} (65 + 2 t - 3 t^{2})

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