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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 h ( x ) = f ( x ) g ( x ) {\displaystyle h(x)={\frac {f(x)}{g(x)}}} , where both f and g are differentiable and g ( x ) ≠ 0. {\displaystyle g(x)\neq 0.}
Quotient Rule is used for determining the derivative of a function which is the ratio of two functions. Visit BYJU'S to learn the definition of quotient rule of differentiation, formulas, proof along with examples.
The quotient rule is a formula that is used to find the derivative of the quotient of two functions. Given two differentiable functions, f (x) and g (x), where f' (x) and g' (x) are their respective derivatives, the quotient rule can be stated as. or using abbreviated notation: Use the quotient rule to find the following derivatives. 1.
Find the derivative of \( \sqrt{625-x^2}/\sqrt{x}\) in two ways: using the quotient rule, and using the product rule. Solution. Quotient rule: \[{d\over dx}{\sqrt{625-x^2}\over\sqrt{x}} = {\sqrt{x}(-x/\sqrt{625-x^2})-\sqrt{625-x^2}\cdot 1/(2\sqrt{x})\over x}.\]
The quotient rule, is a rule used to find the derivative of a function that can be written as the quotient of two functions. More simply, you can think of the quotient rule as applying to functions that are written out as fractions, where the numerator and the denominator are both themselves functions.
Quotient rule in calculus is a method to find the derivative or differentiation of a function given in the form of a ratio or division of two differentiable functions. Understand the method using the quotient rule formula and derivations.
The quotient rule is a method for differentiating problems where one function is divided by another. The premise is as follows: If two differentiable functions, f(x) and g(x), exist, then their quotient is also differentiable (i.e., the derivative of the quotient of these two functions also exists).
What is the quotient rule? The quotient rule is a formula that allows you to differentiate a quotient of two functions (ie one function divided by another) If where u and v are functions of x then the quotient rule is:
The quotient rule allows you to find the derivative of a quotient of two functions – hence the name. The theory behind the calculus quotient rule goes like this: Anytime you have two differentiable functions – let’s use f(x) and g(x) as an example – the quotient must also be differentiable.
Quotient Rule Now that we know the product rule we can find the derivatives of many more functions than we used to be able to. Our next step toward “differentiating everything” will be to learn a formula for differentiating quotients (fractions). The rule is: u u v − uv = v v2 Why is this true?