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The derivative of log a x is I.e. d(log a x)/dx is ??????????????????????????????????? ? ?????

The derivative of logax is I.e. d(logax)/dx is ???????????????????????????????????  ? ?????

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
576-1507_IMG_20190524_214307.jpg
Rajdeep
231 Points
4 years ago
HEY THERE!
 
Here’s your answer:
 
Let \\ y = log_{a}x \\\\y = \frac{log_{e}x}{log_{e}a} \\\\\frac{dy}{dx} = \frac{\frac{1}{x} \times log_{e}a - log_{e}x \times 0}{(log_{e}a)^{2}} \\\\ = \frac{1}{x\times ln (a)}
 
Here I’ve used the quotient rule of differentiation.
If you do not understand any step, please let me know.
THANKS!

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