Verified answer

Do it in two parts:

The 4x

4(x + h) - 4x all over h

= (4x + 4h - 4x)/h

= 4h/h

= 4 no matter what x is

The 3√x

3√(x + h) - 3√x all over h

Multiply top and bottom by 3√(x + h) + 3√x to rationalize the numerator

The top is now 9(x + h) - 9x = 9x + 9h - 9x = 9h

and the bottom is h(3√(x + h) + 3√x)

Cancel the h's to leave 9 over 3√(x + h) + 3√x and as h → 0, this is 9 over 2•3√x

which when x = 4 is 9 over 2•3•2 = 9/12 = 3/4

so f ' (4) = 4 + 3/4 = 19/4