First slide

Derivatives

Question

$If y = \log_{a} x + \log_{x} a + \log_{x} x + \log_{a} a then \frac{d y}{d x} =$

Moderate

A

$\frac{1}{x} + x \log a$
B

$\frac{\log a}{x} + \frac{x}{\log a}$
C

$\frac{1}{x \log a} + x \log a$
D

$\frac{1}{x \log a} - \frac{\log a}{x {(\log x)}^{2}}$

Solution

$\frac{d y}{d x} = \frac{1}{x \log a} - \frac{\log a}{x {(\log x)}^{2}}$

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