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How do you differentiate #y=sin^-1(x/3)#?

Answer 1

#1/sqrt(9-x^2)#

differentiate using the #color(blue)"chain rule"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(sin^-1(f(x)))=1/(sqrt(1-f(x)^2)).d/dx(f(x)))color(white)(2/2)|)))#

#rArrdy/dx=1/(sqrt(1-(x/3)^2)).d/dx(1/3x)#

#=1/(sqrt(1-x^2/9))xx1/3=1/(3sqrt(1/9(9-x^2)#

#=1/sqrt(9-x^2)#

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Answer 2

Scarlett Allison

To differentiate ( y = \sin^{-1}(x/3) ), you use the chain rule of differentiation. The derivative is ( dy/dx = (1/\sqrt{1 - (x/3)^2}) \cdot (1/3) ).

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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.