Differentiate not using first principles

Question

a)   f(x) =  3x³ - 4√x + 1

 

 

b)  f(x)  =  2x (3x² - x) 

 

 

c) f(x) =  (x² + x - 6)  /  (x-2)

Answer 1

I assume means that you need not take the limit of any difference quotient--i.e. rules are to be applied.

 

a) f(x) = 3x3 - 4√x + 1 or f(x) = 3x³ -4x^½ + 1;  f'(x) = 9x² -2x^-½

 

b) f(x) = 6x³ - 2x²  so f'(x) = 18x² - 4x

 

c) f(x) can be simplified to x+3 with 2 excluded from the domain, so f'(x) = 1  but f' is not defined for x=2.