How would you find the first derivative of #f(x) = (5-x)x^(2/3)#?

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How would you find the first derivative of #f(x) = (5-x)x^(2/3)#?

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Answer 1 · 2015-03-31T03:47:10

I would use the Product Rule:
#f'(x)=-1*x^(2/3)+(5-x)2/3x^(-1/3)=#
#=-x^(2/3)+10/3x^(-1/3)-2/3x^(2/3)=#
#=-x^(2/3)[1+2/3]+10/3x^(-1/3)=#
#=-x*x^(-1/3)[5/3]+10/3x^(-1/3)=#
#=-5(x-2)/(3root3(x))#

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How would you find the first derivative of #f(x) = (5-x)x^(2/3)#?

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