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darkknight1
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y = (csc(x) + cot(x) )^-1
Find dy/dx
Find dy/dx
darkknight, you titled this "using chain rule" and Monoxdifly just told you what that is! Are you able to do this now?darkknight said:y = (csc(x) + cot(x) )^-1
Find dy/dx
The chain rule is a mathematical rule used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.
The chain rule is used when finding the derivative of a composite function, where one function is nested inside another. It is also used when finding the derivative of a function that is composed of multiple functions.
To apply the chain rule, you first identify the outer and inner functions of the composite function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function. If there are multiple functions, you continue this process until you have the derivative of the entire composite function.
Sure, let's say we have the function f(x) = (x^2 + 3)^5. We can rewrite this as f(x) = u^5, where u = x^2 + 3. To find the derivative, we use the chain rule and get f'(x) = 5u^4 * u'. Plugging in u = x^2 + 3 and u' = 2x, we get f'(x) = 5(x^2 + 3)^4 * 2x.
Yes, one common mistake is forgetting to take the derivative of the inner function. Another mistake is not properly identifying the inner and outer functions, which can lead to incorrect results. It is important to practice and double check your work when using the chain rule.