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How do you find the derivative of #arcsin(x/2) #?

Answer 1

Charles Arocha

#d/dxsin^(-1)(x/2)=1/(2(sqrt(1-(x^2/4)))#

The rule for differentiation of the inverse sine function states that :

#d/dx sin^(-1)u(x)=1/(sqrt(1-u^2))*(du)/dx#.

So applying this rule in this particular case we get :

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

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Answer 2

Scarlett Allison

To find the derivative of arcsin(x/2), you can use the chain rule. The derivative of arcsin(u) with respect to u is 1/sqrt(1 - u^2). Then, using the chain rule, multiply by the derivative of the inside function, which is 1/2. So, the derivative of arcsin(x/2) with respect to x is (1/2) * (1/sqrt(1 - (x/2)^2)).

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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.