Q. Derivative of $\log_{10}x\ with\ respect\ to\ x^{2}$ is
A) $2x^{2}\log_{e}10$
B) $\frac{\log_{10}e}{2x^{2}}$
C) $\frac{\log_{e}10}{2x^{2}}$
D) $x^{2}\log_{e}10$
Explanation
(b)
Let$\ u = \log_{10}{x\ and\ \ v = x^{2}}$
$\therefore\frac{du}{dx} = \frac{\log_{10}e}{x}\ \ and\ \ \ \ \ \ \frac{\ \ dv}{dx} = 2x$
$\therefore\$ $\frac{du}{dv} = \frac{du\ /dx}{dv\ /dx} = \frac{\log_{10}e}{x}/2x\$
$= \frac{\log_{10}e}{2x^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.