# What is the derivative of y=arccos(1/x)?

Apr 20, 2015

First find the value of siny because siny is going to appear when you use implicit differentiation to find the derivative of the function.

Now differentiate and get the value of $\frac{\mathrm{dy}}{\mathrm{dx}}$.

Apr 20, 2015

The answer is: $y ' = \frac{1}{x \sqrt{{x}^{2} - 1}}$.

y'=-1/sqrt(1-(1/x)^2)*(-1/x^2)=1/(x^2sqrt(1-1/x^2)=

$= \frac{1}{{x}^{2} \sqrt{\frac{{x}^{2} - 1}{x} ^ 2}} = \frac{1}{{x}^{2} \cdot \frac{1}{x} \cdot \sqrt{{x}^{2} - 1}} =$

$= \frac{1}{x \sqrt{{x}^{2} - 1}}$.