quotient rule
The quotient rule is a rule used in calculus to find the derivative of a function that is the quotient of two other functions
The quotient rule is a rule used in calculus to find the derivative of a function that is the quotient of two other functions. It is used when you have a function f(x) that can be expressed as f(x) = g(x) / h(x), where g(x) and h(x) are differentiable functions.
The quotient rule states that the derivative of f(x) can be found using the formula:
f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2
Let’s break down the components of this formula:
– g'(x): This represents the derivative of the numerator function g(x) with respect to x. It tells us the rate at which g(x) is changing or the slope of the tangent line to the graph of g(x) at a given point.
– h'(x): This represents the derivative of the denominator function h(x) with respect to x. Like g'(x), it tells us the rate at which h(x) is changing or the slope of the tangent line to the graph of h(x) at a given point.
– h(x)^2: This term represents the square of the denominator function h(x). It is included in the denominator to account for the fact that we are dividing by h(x).
To use the quotient rule, you should follow these steps:
1. Identify the numerator function g(x) and the denominator function h(x) in the given function f(x).
2. Compute the derivatives g'(x) and h'(x) by differentiating g(x) and h(x) separately using the rules of differentiation.
3. Substitute the values of g'(x), h(x), g(x), and h'(x) into the quotient rule formula.
4. Simplify the expression obtained in step 3, if possible, by combining like terms or factoring out common factors.
By following these steps and applying the quotient rule, you can find the derivative of a function that is a quotient of two other functions.
More Answers:
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