Question

What’s the definition of “quotient rule” In math please give a definition & example thank u

Answer 1

Quotient rule:

The Quotient Rule says that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

The quotient rule is,

`(d)/(dx)((u)/(v))=(vu^(\prime)-uv^(\prime))/(v^2)`

Here, u and v are the functions of the same independent variable.

Example:

Let us take the problem,

`y=(\sin x)/(\cos x)`

Differentiating with respect to x using the quotient rule is,

`\begin{gathered} (dy)/(dx)=(\cos x\cdot(d(\sin x))/(dx)-\sin x\cdot(d(\cos x))/(dx))/((\cos x)^2) \\ =(\cos x(\cos x)-\sin x(-\sin x))/(\cos ^2x) \\ =\frac{\cos ^2x_{}+\sin ^2x}{\cos ^2x} \\ =(1)/(\cos ^2x) \\ =\sec ^2x \end{gathered}`