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Find the second order derivative if y=e^2x^2.(a) 4e^2x^2 (4x^2+3)(b) 4e^2x^2 (4x^2-1)(c) 4e^2x^2 (4x^2+1)(d) e^2x^2 (4x^2+1)The question was posed to me in an interview for job.The question is from Second Order Derivatives in division Continuity and Differentiability of Mathematics – Class 12

Answer»

Correct answer is (C) 4e^2x^2 (4x^2+1)

To EXPLAIN: GIVEN that, y=E^2x^2

\(\frac{DY}{dx}\)=e^2x^2.4x

By using u.v rule, we get

\(\frac{d^2 y}{dx^2}=\frac{d}{dx} (e^{{2x}^2}).4x+\frac{d}{dx} (4x).e^{{2x}^2}\)

16x^2 e^2x^2+4e^2x^2=4e^2x^2 (4x^2+1)


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