What is the derivative of log_{10}((1+x)/n) ?

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

What is the first derivative of log_{10}((1+x)/n) ?

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

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derivative of

lo g_{10} (\frac{1 + x}{n})

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{\frac{1 + x}{n}} \frac{d}{d x} (\frac{1 + x}{n})

= \frac{1}{\frac{1 + x}{n}} \frac{d}{d x} (\frac{1 + x}{n})

\frac{d}{d x} (\frac{1 + x}{n}) = \frac{1}{n}

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

Simplify

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

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

\frac{x ^{2}}{a ^{2}}

3 sin^{2} (x) + 3 cos^{2} (x)

\frac{ln ( x ^{2} )}{2}

f (x) = tan^{2} (sin (x))

\frac{d}{d x} (sin^{3} (lo g_{10} (x)))

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