How do you find the derivative of #sqrt(4-x^2)#?

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Answer 1 · 2015-05-23T01:46:27

Using chain rule, by naming #u=4-x^2#.

Before starting, let's just rewrite your fucntion

#y=(4-x^2)^(1/2)=u^(1/2)#

Now, as the chain rule states that

#(dy)/(dx)=(dy)/(du)(du)/(dx)#

#(dy)/(du)=1/(2u^(1/2))#

#(du)/(dx)=-2x#

Now

#(dy)/(dx)=1/(2u^(1/2))*(-2x)#

#(dy)/(dx)=(-cancel(2)x)/(cancel(2)u^(1/2))#

Substituting #u#:

#(dy)/(dx)=-x/(4-x^2)^(1/2)=-x/(sqrt(4-x^2))#