Use the quotient rule to find the derivative of the following function.𝑓(𝑥)=𝑥+1𝑥−6

The quotient rule for differentiation states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the square of the denominator.

So, if we have a function f(x) = (x+1)/(x-6), we can apply the quotient rule to find its derivative.

Step 1: Identify the numerator and the denominator. Numerator (u) = x + 1 Denominator (v) = x - 6

Step 2: Find the derivative of the numerator and the denominator. u' = derivative of (x + 1) = 1 v' = derivative of (x - 6) = 1

Step 3: Apply the quotient rule. f'(x) = (v * u' - u * v') / (v^2) f'(x) = ((x - 6) * 1 - (x + 1) * 1) / ((x - 6)^2) f'(x) = (x - 6 - x - 1) / ((x - 6)^2) f'(x) = (-7) / ((x - 6)^2)

So, the derivative of the function f(x) = (x+1)/(x-6) is f'(x) = -7 / (x - 6)^2.