What is the quotient rule?

Answer 1

See explanation.

The following formula, known as the Quotient Rule, can be used to get the derivative of the quotient of two differentiable functions:

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Answer 2

Paisley Johnson

The quotient rule is a formula used in calculus to find the derivative of a quotient of two functions. It states that if you have two differentiable functions ( f(x) ) and ( g(x) ), the derivative of their quotient ( \frac{f(x)}{g(x)} ) is given by:

[ \left( \frac{f(x)}{g(x)} \right)' = \frac{f'(x) \cdot g(x) - f(x) \cdot g'(x)}{(g(x))^2} ]

Where ( f'(x) ) and ( g'(x) ) represent the derivatives of ( f(x) ) and ( g(x) ), respectively.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.