Question

If g(x)= square root of 3-5x, find the domain of g'(x).

Answer 1

Answer: Check the pic

Step-by-step explanation:

Answer 2

Answer:

domain: x>3/5

Step-by-step explanation:

First we need to derive our function g(x) to get a new function g'(x)

To do this we will have to apply chain rule because we have an inner and outer functions.

Our G(x) = square root(3-5x)

Chain rule formula states that: d/dx(g(f(x)) = g'(f(x))f'(x)

where d/dx(g(f(x)) = g'(x)

g(x) is the outer function which is x^1/2

f(x) is our inner function which is 3-5x

therefore f'(x)= 1/2x^(-1/2) and f'(x) = -5

g'(f(x)) = -1/2(3-5x)^(-1/2)

Applying chain rule then g'(x) = 1/2 (3-5x)^(-/1/2)*(-5)

But the domain is the values of x where the function g'(x) is not defined

In this case it will be 3-5x > 0, because 3-5x is a denominator and anything divide by zero is infinity/undefined

which gives us x >3/5