Please help, I have no idea where to start.
Use the quotient rule to find the derivative.
f(x)= ((x+4)/(x-2))
f '(x) =
Thank u!
To find the derivative of the function f(x) = (x + 4)/(x - 2) using the quotient rule, you'll need to remember the formula:
If you have a function f(x) = u(x)/v(x), then the derivative f '(x) is given by:
f '(x) = (v(x) * u'(x) - u(x) * v'(x))/(v(x))^2
Now let's apply the quotient rule to find the derivative of f(x) = (x + 4)/(x - 2):
Step 1: Identify u(x) and v(x):
In our case, u(x) = x + 4 and v(x) = x - 2.
Step 2: Find u'(x) and v'(x):
To determine the derivatives of u(x) and v(x), you need to differentiate each term independently.
u'(x) = 1 (since the derivative of x + 4 with respect to x is 1)
v'(x) = 1 (since the derivative of x - 2 with respect to x is 1)
Step 3: Apply the quotient rule formula:
Substitute the values into the quotient rule formula to find f '(x):
f '(x) = (v(x) * u'(x) - u(x) * v'(x))/(v(x))^2
= ((x - 2)(1) - (x + 4)(1))/((x - 2))^2
= (x - 2 - (x + 4))/((x - 2)(x - 2))
= (x - 2 - x - 4)/(x^2 - 4x + 4)
= (-6)/((x^2 - 4x + 4))
So, the derivative of f(x) = (x + 4)/(x - 2) using the quotient rule is f '(x) = -6/(x^2 - 4x + 4).