Question

Apply the quotient rule to differentiate the following.Use the rule:
f(x)/g(x) y=f’(x)•g(x)-f(x)•g’(x)/[g(x)]^2.

1) y= 6x/2-x

Answer 1

To differentiate y = 6x / (2 - x) using the quotient rule, we will let f(x) = 6x and g(x) = (2 - x).

Now, we will find the derivative of f(x) and g(x):

f'(x) = 6 (the derivative of 6x with respect to x)

g'(x) = -1 (the derivative of (2 - x) with respect to x)

Now we will apply the quotient rule:

y' = [f'(x) • g(x) - f(x) • g'(x)] / [g(x)]^2

= [6 • (2 - x) - 6x • (-1)] / (2 - x)^2

= (12 - 6x + 6x) / (2 - x)^2

= 12 / (2 - x)^2

So, the derivative of y = 6x / (2 - x) is y' = 12 / (2 - x)^2.