How do you use the limit definition to find the derivative of #f(x)=3x^(2/3)-4x^(1/2)-2#?

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Answer 1 · 2017-01-20T14:36:35

I would first use the limit definition to show that the derivative of a sum is the sum of the derivatives.

Then I could use the definition to show that

the derivative of #3x^(2/3)# is #2x^(-1/3)# and

the derivative of #-4x^(1/2)# is #-2x^(-1/2)# and

the derivative of #-2# is #0#.

Therefore the derivative of #f(x)# is

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