Here are the essential concepts you must grasp in order to answer the question correctly.
Quotient Rule
The quotient rule is a fundamental principle in calculus used to differentiate functions that are expressed as the ratio of two other functions. It states that if you have a function f(x) = g(x)/h(x), the derivative f'(x) can be found using the formula f'(x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))². Understanding this rule is essential for simplifying expressions involving division.
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Radical Expressions
Radical expressions involve roots, such as square roots, cube roots, etc. In the context of the given question, √(x²/144y¹²) can be simplified by applying the property that √(a/b) = √a/√b. This concept is crucial for simplifying expressions under a square root and understanding how to manipulate them algebraically.
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Simplification of Fractions
Simplifying fractions involves reducing them to their lowest terms by dividing the numerator and denominator by their greatest common factor (GCF). In the expression √(x²/144y¹²), recognizing that both the numerator and denominator can be simplified separately is key to achieving a more manageable form. This concept is foundational in algebra for making expressions easier to work with.
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