If f(x) = 16 sqrt x, then f'(4) is equal to...

Answer 1

To differentiate f(x) = 16√x it's easier to put it into an exponential format.

The power rule states that if f(x) = xⁿ then g'(x) = nx^n-1

f(x) = 16√x = 16x^1/2

so n = 1/2

Using the power rule

f'(x) = (1/2)(16)x^1/2-1 = 8x^-1/2 = (8)/(x^1/2) = (8) / (√x)

So f'(4) = (8) / (√4) = 8/2 = 4