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

1 Answer
Jim G.
Aug 29, 2016

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

Explanation:

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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