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What is the derivative of #sqrt(4-x^2)#?

Answer 1
Christopher AllersChristopher Allers

#(-x)/(sqrt(4-x^2))#

Differentiate using a combination of #color(blue)"power and chain rule"#
#color(orange)"Reminder of chain rule"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))........ (A)#
let #u=4-x^2rArr(du)/(dx)=-2x#
and #y=u^(1/2)rArr(dy)/(du)=1/2u^(-1/2)#

substitute these values into (A) converting u back into terms of x.

#rArrdy/dx=1/2u^(-1/2).(-2x)=(-x)/(sqrt(4-x^2))#
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Answer 2
Aurora AlvaradoAurora Alvarado

The derivative of sqrt(4-x^2) is -x/sqrt(4-x^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.

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.

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.

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.

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