What is the derivative of #x*x^(1/2)#?

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What is the derivative of #x*x^(1/2)#?

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Answer 1 · 2016-03-18T15:56:40

#=3/2x^(1/2)#

Explanation:

#d/dx(x*x^(1/2))=d/dx(x^(1/2+1))=d/dx(x^(3/2))=3/2x^(3/2-1)=3/2x^(1/2)#

Answer 2 · 2016-03-18T16:01:56

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

Explanation:

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

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What is the derivative of #x*x^(1/2)#?

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