Consider a function F (x) given by the following equation: F(x) = f(x)/g(x) where f(x) and g(x) are two functions such that limx→0 f(x) = limx→0 g(x) = 0. (a)  What rule do you need to get F′(x)? Write out and expression of F′(x) with respect to f and g.   (b) What rule do you need to get limx→0F(x)? Write out and expression of limx→0 F(x) with respect to f and g.   Find the derivative of f(x) = x^x^x Please show all your work and step by step.

Consider a function F (x) given by the following equation: F(x) = f(x)/g(x)

where f(x) and g(x) are two functions such that limx→0 f(x) = limx→0 g(x) = 0.

(a)  What rule do you need to get F′(x)? Write out and expression of F′(x) with respect to f and g.

(b) What rule do you need to get limx→0F(x)? Write out and expression of limx→0 F(x) with respect to f and g.

Find the derivative of

f(x) = x^x^x

Please show all your work and step by step.