Calculus Revision Help: Derivative problem
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Calculus Revision Help: Derivative problem

[From: ] [author: ] [Date: 12-05-12] [Hit: ]
If you could please explain how you get the derivative,Combine some like terms and what not and you should end up with the right answer-sqrt(1-x) = (1-x)^.Use the product rule to do the derivative of x*(1-x)^.5-f(x)= sqrt(1-x) - x * 0.just use the product rule, with the chain rule!......
Hi, I can't seem to get the right derivative. If you could please explain how you get the derivative, would be great :)

f(x) = x square root (1-x)

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Combinaiton of product rule and chain rule:

(x)(d/dx(√1-x)) + d/dx(x)(√(1-x))

x (1/2(1-x)^(-1/2)) + (1)(1-x)^(1/2)

Combine some like terms and what not and you should end up with the right answer

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sqrt(1-x) = (1-x)^.5
Use the product rule to do the derivative of x*(1-x)^.5

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f'(x)= sqrt(1-x) - x * 0.5*(1-x)^(-1/2)

just use the product rule, with the chain rule!

be aware of the sign - comming from the inner (1-x) derivate
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