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Popular Calculus >

derivative of (ln(x-10)/(ln(10)))

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (10) = 0

= \frac{1}{ln ( 10 )} (\frac{1}{x} - 0)

Simplify

\frac{1}{ln ( 10 )} (\frac{1}{x} - 0) : \frac{1}{ln ( 10 ) x}

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

Graph

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Frequently Asked Questions (FAQ)

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