Find the Differentiate

Question

g(x) =5e^x√x

Answer 1

g(x) = 5e^x√x

Use the product rule:

g'(x) = 5e^x√x + 5e^x[(1/2)x^-1/2] = 5e^x[√x + 1/(2√x)] = 5e^x[(2x+1) / (2√x)]

Answer 2

First, note that we can rewrite the original function as g(x)=(5e^x)(x^(1/2)).

The function g(x) is a product of two functions of x, so we need to use the product rule to differentiate g(x). Using basic derivative rules, we get the following:

g'(x)=(5e^x)((1/2)x^(-1/2))+(x^(1/2))(5e^x)

or

g'(x)=(5e^x)(1/(2√x)+√x).

Hope this helps!