Question

If h(x) =x+2/x-2, then dy/dx= ?​

Answer 1

Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.

Using this rule, we can find the derivative of h(x) as follows:

h(x) = (x + 2) / (x - 2)

h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator

h'(x) = (-2 - 2x) / (x - 2)^2

Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.

Explanation:

Answer 2

To find dy/dx, we can use the quotient rule:

dy/dx = [(x - 2)(1) - (x + 2)(1)]/(x - 2)^2

Simplifying the numerator:

dy/dx = (-4)/(x - 2)^2

So the derivative of h(x) with respect to x is -4/(x - 2)^2.