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jtt
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Homework Statement
Find the derivative of the following:
Homework Equations
Y= x^3(5x-1)^4
The Attempt at a Solution
4(3x^2(5x-1)^3)(4(3x^2(3(5x-1)^2)(2(5x-1)(5)
Differentiation by the chain rule is a method used in calculus to find the derivative of a composite function, where one function is inside another. It allows you to find the rate of change of one quantity with respect to another quantity.
To use the chain rule, you must first identify the inner function and the outer function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function. This will give you the derivative of the composite function.
The chain rule is important because it allows us to find the derivative of more complex functions that cannot be easily differentiated using basic rules. It is a fundamental tool in calculus and is used in many real-world applications.
One common mistake when using the chain rule is forgetting to take the derivative of the inner function. Another mistake is not properly distributing the derivative of the outer function to the entire inner function. It is important to pay attention to the order of operations and to carefully apply the rule.
Yes, the chain rule can be used to find higher order derivatives. To find the second derivative, you would first find the first derivative using the chain rule, and then apply the chain rule again to find the second derivative. This process can be continued for any desired order of the derivative.