SOLUTION: find the (nth) derivative of. y= x^n * sqrt(x)

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Question 1141301: find the (nth) derivative of. y= x^n * sqrt(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28d%2Fdx%29%28+x%5En%2Asqrt%28x%29%29+=

apply the product rule : %28f%2Ag%29'=f '*g+f*g', where f=x%5En, g=+sqrt%28x%29



since

%28d%2Fdx%29%28x%5En%29=nx%5E%28n-1%29+and %28d%2Fdx%29%28sqrt%28x%29%29=1%2F2sqrt%28x%29, we have




since +x%5E%28n-1%29sqrt%28x%29=x%5E%28n-1%29x%5E%281%2F2%29+=x%5E%28n-1%2F2%29+and





%28d%2Fdx%29%28x%5En+%2Asqrt%28x%29%29+=nx%5E%28n-1%2F2%29+%2B%281%2F2%29x%5E%28n+-+1%2F2%29.........factor out x%5E%28n+-+1%2F2%29


%28d%2Fdx%29%28x%5En+%2Asqrt%28x%29%29+=+%28n+%2B+1%2F2%29+x%5E%28n+-+1%2F2%29