The equation x^2y + y^3 = 10 defines y implicitly. What is dy/dx at the point (1, 2)?
Correct answer: A. -4/13
- A. -4/13
- B. -3/13
- C. 4/13
- D. 3/13
Explanation
Differentiation gives 2xy + x^2(dy/dx) + 3y^2(dy/dx) = 0. At (1, 2), this becomes 4 + 13(dy/dx) = 0, so dy/dx = -4/13.
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About Differentiation and Optimisation
Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
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