SOLUTION: please help me with this question If f(x) = x*sqr(9-x^2) find f'(x)

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Question 1154502: please help me with this question
If f(x) = x*sqr(9-x^2) find f'(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%2Asqr%289-x%5E2%29
to find f'%28x%29 apply the Product Rule : %28f%2A+g+%29'=f '*g+f%2A+g'

f'%28x%29=%28d%2Fdx%29x%2Asqrt%289+-+x%5E2%29%2Bx%2A+%28d%2Fdx%29sqrt%289+-+x%5E2%29

f'%28x%29=1%2Asqrt%289+-+x%5E2%29%2Bx%2A+%28d%2Fdx%29sqrt%289+-+x%5E2%29.......%28sqrt%289-x%5E2%29%29' =-+x%2F%28sqrt%289-x%5E2%29%29

f'%28x%29=1%2Asqrt%289+-+x%5E2%29%2Bx%2A+%28-+x%2F%28sqrt%289-x%5E2%29%29%29

f'%28x%29= sqrt%289+-+x%5E2%29-+x%5E2%2F%28sqrt%289-x%5E2%29%29

f'%28x%29= %28sqrt%289+-+x%5E2%29%29%5E2%2F%28sqrt%289-x%5E2%29%29-+x%5E2%2F%28sqrt%289-x%5E2%29%29

f'%28x%29= %289+-+x%5E2-+x%5E2%29%2F%28sqrt%289-x%5E2%29%29

f'%28x%29= %289+-+2x%5E2%29%2F%28sqrt%289-x%5E2%29%29