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Limits and Derivatives · JEE Preparation Mathematics

If y=(x^2+1)(x^3-2), find frac{dy}{dx} at x=1.

Practice question from Limits and Derivatives (JEE Preparation Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-955CAE

If y=(x2+1)(x3−2)y=(x^2+1)(x^3-2), find dydx\frac{dy}{dx} at x=1x=1.

  1. A.2
  2. B.3
  3. C.4Correct answer
  4. D.6

Solution

Using the product rule, dydx=2x(x3−2)+3x2(x2+1)\frac{dy}{dx}=2x(x^3-2)+3x^2(x^2+1). At x=1x=1, this equals 2(1)(−1)+3(1)(2)=42(1)(-1)+3(1)(2)=4.

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