Question

The differential coefficient of ${\log }_{10}x$ with respect to is ${\log }_{x}10$

• A. $\frac{x^2}{100}$
• B. ${\left({\log }_{x}10\right)}^2$
• C. $-{\left({\log }_{10}x\right)}^2$
• D. 1

Answer 1

Answer: (C)

$\frac{\frac{d}{dx}\left(\frac{{\log }_e^x}{{\log }_e^{10}}\right)}{\frac{d}{dx}\left(\frac{{\log }_e^{10}}{{\log }_e^x}\right)}=-{\left(\frac{{\log }_e^x}{{\log }_e^{10}}\right)}^2=-{\left({\log }_{10}^x\right)}^2$