SOLUTION: What is the derivative of y = r / sqrt root of r^2 + 1

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Question 1140604: What is the derivative of y = r / sqrt root of r^2 + 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the derivative of
y+=+r+%2F+sqrt%28r%5E2+%2B+1+%29

%28d%2Fdr%29+%28+r+%2F+sqrt%28r%5E2+%2B+1+%29%29=
Apply the Quotient Rule :
%28f%2Fg%29%27=+%28f%27%2Ag-g%27%2Af%29%2Fg%5E2+

= ....since %28d%2Fdr%29%28r%29=1 and %28d%2Fdr%29%28sqrt%28r%5E2%2B1%29%29+=r+%2F+sqrt%28r%5E2+%2B+1+%29 , we have

=

Simplify : +%28sqrt%28r%5E2%2B1%29-%28r%2Fsqrt%28r%5E2%2B1%29%29r%29%2F%28sqrt%28r%5E2%2B1%29%5E2%29: you will get

=1%2F%28%28r%5E2%2B1%29sqrt%28r%5E2%2B1%29%29+

or

=1%2Fsqrt%28%28r%5E2%2B1%29%5E3%29+

or

=1%2F%28r%5E2%2B1%29%5E%283%2F2%29+