How do you use the definition of a derivative to find the derivative of #f(x) = 6 x + 2 /sqrt{x}#?

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Answer 1 · 2016-01-10T14:02:29

# 6 - 1/x^(3/2) #

#f(x) =6x + 2/sqrtx= 6x + 2/x^(1/2) = 6x + 2x^(-1/2) #

we have now written #2/sqrtx # in the correct form to be differentiated.

# f(x) ax^n rArr f'(x) = nax^(n - 1 ) #

differentiating gives :

#f'(x) = 6 + 2(-1/2) x^(-3/2) = 6 - 1/x^(3/2) #

rewriting the negative index as a positive index.