Stumped. Differentiate the function: f(x) = 5e^x + (4 / cuberoot(x))

f(x) = 5e^x + (4 / cuberoot(x))

I realize that the 5e^x is it's own derivative, so it's mainly the fraction and applying the quotient rule there that I am having trouble with. Where's the calculus geeks?

You don't need the quotient rule. The 4 is just a constant, you have 4 * x^(-1/3). Use the power rule, the derivative of x^n is n * x^(n-1) with n = -1/3.

You COULD use the quotient rule, it's just overkill since you don't have a quotient of functions. It would work like this.

f(x) = 4/x^(1/3) = g(x)/h(x)

So g(x) = 4, g'(x) = 0
h(x) = x^(1/3), h'(x) = (1/3)x^(-2/3)

f'(x) = [h(x) g'(x) - g(x) h'(x)] / h(x)^2. Just plug all those things in.

= [x^(1/3) * 0 - 4 * (1/3) * x^(-2/3)] / x^(2/3)

f(x) = 5e^(x) + (4/x^(1/3))

f '(x) = 5e^(x) -4/3x^(-4/3)