How to Use Quotient and Product Rule to Find Derivatives | First Derivative Help

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In summary, the quotient rule is a formula used to find the derivative of a quotient of two functions, while the product rule is used to find the derivative of a product of two functions. The quotient rule states that the derivative of f(x)/g(x) is given by (g(x)f'(x) - f(x)g'(x)) / (g(x))^2, while the product rule states that the derivative of f(x)g(x) is given by f'(x)g(x) + f(x)g'(x). To apply the quotient rule, you must first identify the two functions in the quotient and use the formula. The quotient rule can only be used for two functions, while the product rule can be used
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Homework Statement


differentiate the following function using both the quotient and product rule with respect to their independent variable(s) and simplify your answer


Homework Equations


AC= (Q+1)^(0.5) / Q


The Attempt at a Solution


product rule:
dac/dQ = [(Q+1)^(0.5) x (-q^-2) ] + [ 0.5(Q+1)^(1/2) ]
dac/dQ = Q^(-1.5) + 1 + 0.5(Q+1)^(1/2)
 
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I think you are just supposed to show that d/dQ of (Q+1)^(1/2)/Q taken with the quotient rule, and d/dQ of (Q+1)^(1/2)*Q^(-1) taken with the product rule are equal. But I'm really not sure how you are getting those expressions you show. Can you show us?
 

FAQ: How to Use Quotient and Product Rule to Find Derivatives | First Derivative Help

What is the quotient rule?

The quotient rule is a formula used to find the derivative of a quotient of two functions. It states that the derivative of f(x)/g(x) is given by (g(x)f'(x) - f(x)g'(x)) / (g(x))^2.

What is the product rule?

The product rule is a formula used to find the derivative of a product of two functions. It states that the derivative of f(x)g(x) is given by f'(x)g(x) + f(x)g'(x).

How do I apply the quotient rule to find derivatives?

To apply the quotient rule, you must first identify the two functions in the quotient. Then, use the formula (g(x)f'(x) - f(x)g'(x)) / (g(x))^2 to find the derivative.

Can I use the quotient rule to find derivatives of more than two functions?

No, the quotient rule can only be used for the derivative of a quotient of two functions. If you have more than two functions, you will need to use the chain rule or other derivative rules.

How is the product rule different from the quotient rule?

The product rule is used for finding the derivative of a product of two functions, while the quotient rule is used for finding the derivative of a quotient of two functions. They have different formulas and cannot be used interchangeably.

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