Question

Given f(x)=(3x²-4x)/(x²-5), differentiate AND simplify .

Answer 1

To differentiate the given function, use the quotient rule and simplify the expression.

Step-by-step explanation:

To differentiate the function f(x)=(3x²-4x)/(x²-5), we can use the quotient rule.

First, differentiate the numerator: d/dx(3x²-4x) = 6x-4.

Then, differentiate the denominator: d/dx(x²-5) = 2x.

Using the quotient rule, the derivative of f(x) is (6x-4)(x²-5) - (3x²-4x)(2x) / (x²-5)².

To simplify this expression further, you can expand and combine like terms.