# Quotient Rule

Quotient rule provides a method to find the derivative of a function which is expressed in the form of quotient of two functions, like h(x) = $\frac{f(x)}{g(x)}$. Just as the derivative of a product function is not found by multiplying the derivatives of its factors, we can intuitively say that the derivative of a quotient is not the quotient of the derivatives. Let us verify this with an example.

Let f(x) = $x^3$. Using the power rule for derivatives we know f'(x) = $3x^2$. But if we choose to express f(x) as $\frac{x^{4}}{x}$, the derivative of $x^4$= $4x^3$ and the derivative of x = 1. The quotient of derivatives = $\frac{4x^3}{1}$ = $4^x^3$which is not the derivative of f(x). The quotient rule for derivatives is derived from the limit definition of differential coefficient by applying laws of limits.

Other than the quotient rule for derivatives, different quotient rules exist for different concepts like the quotient rule for exponents and logarithms, quotient rule for limits. Let us state and prove the quotient rule for derivatives and also solve few example problems.