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What is the derivative of #g(x)= x^2*sqrt(1-x^2)#?

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Apr 14, 2015

The answer is: #y'=(2x-3x^3)/sqrt(1-x^2)#.

For the product rule:

#y'=2x*sqrt(1-x^2)+x^2*1/(2sqrt(1-x^2))*(-2x)=#

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

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

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