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

Answer 1

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 #dy/dx#.

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Answer 2

Aurora Alvarado

The answer is: #y'=1/(xsqrt(x^2-1))#.

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

#=1/(x^2sqrt((x^2-1)/x^2))=1/(x^2*1/x*sqrt(x^2-1))=#

#=1/(xsqrt(x^2-1))#.

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Answer 3

Elijah Abram

The derivative of ( y = \arccos\left(\frac{1}{x}\right) ) with respect to ( x ) is ( \frac{d}{dx}\left(\arccos\left(\frac{1}{x}\right)\right) = \frac{1}{x \sqrt{x^2 - 1}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.