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exmachina
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Homework Statement
http://i.imgur.com/TSLwA.png
Homework Equations
The Attempt at a Solution
Sorry I figured it out, it was the product rule.
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The Product Rule is a formula used in calculus to find the derivative of two functions that are multiplied together. It states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.
The Product Rule should be used when you have a function that is a product of two other functions, and you need to find its derivative. It is also useful when differentiating expressions that involve variables raised to different powers, such as x^2 * y^3.
To apply the Product Rule, you must first identify the two functions that are being multiplied together. Then, use the formula "f'(x)g(x) + f(x)g'(x)" where f'(x) is the derivative of the first function and g'(x) is the derivative of the second function. Substitute the functions and their derivatives into the formula and simplify to find the derivative of the product.
One common mistake is forgetting to take the derivative of one of the functions. Make sure to find the derivative of both functions and include them in the formula. Another mistake is mixing up the order of the functions in the formula, which will result in an incorrect answer. Be sure to follow the correct order of "f'(x)g(x) + f(x)g'(x)" when using the Product Rule.
Yes, the Product Rule can be extended to more than two functions. For example, when differentiating f(x)g(x)h(x), you would use the formula "f'(x)g(x)h(x) + f(x)g'(x)h(x) + f(x)g(x)h'(x)". Each term in the formula represents the derivative of one of the functions multiplied by the remaining functions. This can be extended to any number of functions being multiplied together.