Question

Use quotient rule to find the derivative of g(x)= x²/(x-11)

Answer 1

To find the derivative of g(x) = x²/(x-11) using the quotient rule, we substitute the values into the formula and simplify to obtain g'(x) = (x²-22x)/(x-11)².

Step-by-step explanation:

To find the derivative of g(x) = x²/(x-11) using the quotient rule, we first need to identify the numerator and denominator.

Let f(x) = x² and g(x) = (x-11).

Using the quotient rule, the derivative of g(x) is given by:

g'(x) = (f'(x) * g(x) - f(x) * g'(x)) / (g(x))²

Substituting the values into the quotient rule formula, we get:

g'(x) = ((2x*(x-11)) - (x²) * (1))/(x-11)²

Simplifying further, we have:

g'(x) = (2x²-22x-x²)/(x-11)²

Combining like terms, the final derivative of g(x) is:

g'(x) = (x²-22x)/(x-11)².