Math help?

Question

If f(x) = 3 \sqrt{x} (x^3- 4 \sqrt {x} +2 ), find f'( 16 ).

Answer 1

Multiply this out *before* taking a derivative and you will get a linear combination of powers of x. This is an easy derivative:
f(x) = 3*x^(7/2) + 12*x +6*x^(1/2)

Remember that (x^a)' = a*(x^(a-1)) for all nonzero a, not just integers.