Differentiation
Student Question
What is differentiation?
Sia Response
Explanation
Differentiation is the process of finding the derivative of a function, which represents the rate at which the function's value changes with respect to changes in its input variable.
Solution
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Step 1: To differentiate the function (Y^2)/(x) with respect to x, we apply the quotient rule.
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Step 2: The quotient rule states that ((f)/(g))' = (f'g - fg')/(g^2) , where f = Y^2 and g = x . Since Y is treated as a constant with respect to x , f' = 0.
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Step 3: Applying the quotient rule, we get (d)/(dx)((Y^2)/(x)) = (0 · x - Y^2 · 1)/(x^2).
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Step 4: Simplifying the expression, we obtain -(Y^2)/(x^2) , assuming x neq 0.
Answer
-(Y^2)/(x^2)
Key Concept
Differentiation
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