Question

2-x/ x^2 find the derivatives by quotient role​

Answer 1

Answer:

The quotient rule states that the derivative of a function h(x) where h(x) = f(x)/g(x) is h'(x) = (g(x)f'(x) - f(x)g'(x))/(g(x))2.

For example, let h(x)=x2/4x3-7. Our functions f and g are f(x)=x2 and g(x)=4x3-7. By using normal differentiating rules, we know that f'(x)=2x and g'(x)=12x2. Plug these values into the formula: h'(x)=((4x3-7)(2x) - (x2)(12x2))/(12x2)2. By expanding, we get h'(x)=(8x4-14x - 12x4)/144x4 = (-4x4-14x)/144x4. Simplified, this becomes h'(x)=(-2x3-7)/72x3.