Differentiation Question 77
Question: If $ y={\log _{10}}x^{2} $ , then $ \frac{dy}{dx} $ is equal to
Options:
A) $ \frac{2}{x} $
B) $ \frac{2}{x{\log _{e}}10} $
C) $ \frac{1}{x{\log _{e}}10} $
D) $ \frac{1}{10x} $
Show Answer
Answer:
Correct Answer: B
Solution:
Given $ y={\log _{10}}x^{2} $
$ y=\frac{{\log _{e}}x^{2}}{{\log _{e}}10} $ , $ ( \because {\log _{a}}b=\frac{{\log _{e}}b}{{\log _{e}}a} ) $
$ y=\frac{2{\log _{e}}x}{{\log _{e}}10} $ ,
$ \therefore \frac{dy}{dx}=\frac{2}{x{\log _{e}}10} $ .
BETA
