Question

If $y={\log }_{a}x,x>0,$ then, $\frac{dy}{dx}$ is equal to:

• A. $\frac{1}{x}$
• B. $\frac{1}{ax}$
• C. $\frac{1}{x}{\log }_{x}a$
• D. $\frac{1}{a}{\log }_{e}x$
• E. $\frac{1}{x}{\log }_{a}e$

Answer 1

Answer: (E)

$y={\log }_{a}x,$ $x>0$ $\Rightarrow$ $y=\frac{\log x}{\log a},x>0$ $\Rightarrow$ $\frac{dy}{dx}=\frac{1}{x\log a},x>0$ $=\frac{1}{x}{\log }_{a}e$