Question

quoficent rule of diffrensation​

Answer 1

Answer:

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions.[1][2][3] Let

${\displaystyle f(x)=g(x)/h(x),}{\displaystyle f(x)=g(x)/h(x),}$

where both g and h are differentiable and

${\displaystyle h(x)\neq 0.}{\displaystyle h(x)\neq 0.}$

The quotient rule states that the derivative of f(x) is

${\displaystyle f'(x)={\frac {g'(x)h(x)-g(x)h'(x)}{[h(x)]^{2}}}.}f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{[h(x)]^2}.$

Examples :

${\displaystyle {\begin{aligned}{\frac {d}{dx}}{\frac {e^{x}}{x^{2}}}&={\frac {\left({\frac {d}{dx}}e^{x}\right)(x^{2})-(e^{x})\left({\frac {d}{dx}}x^{2}\right)}{(x^{2})^{2}}}\\&={\frac {(e^{x})(x^{2})-(e^{x})(2x)}{x^{4}}}\\&={\frac {e^{x}(x-2)}{x^{3}}}.\end{aligned}}}</p><p>$