Question

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

Answer 1

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

Explanation:

`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.