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Calculus and Analysis
Differential Calculus
Analyzing functions

Halkadvalseln

Answered question

2021-11-18

Derivatives of logarithmic functions Calculate the derivative of the following functions. In some cases, it is useful to use the properties of logarithms to simplify the functions before computing

f^{'} 1 x 2

y = \log_{l 0} {x}

Answer & Explanation

Himin1945

Beginner2021-11-19Added 12 answers

Step 1
Given function is

y = \log_{l 0} {x}

.
From Property of logarithm, we have

\log_{a} {b} = \frac{\ln b}{\ln a}

Therefore, given function can be written as:

y = \log_{l 0} {x}

= \frac{\ln x}{\ln 10}

Differentiating the given function with respect to x,

\frac{d y}{d x} = \frac{d}{d x} [\frac{\ln x}{\ln 10}]

= \frac{1}{\ln 10} \cdot \frac{1}{x}

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

Step 2
Hence, required derivative of the function is

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

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