A particle moves along the curve defined by

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A particle moves along the curve defined by y=ex2y=e^{x^{2}}, where xx depends on time according to x(t)=ln⁡(1+3t)x(t)=\ln(1+3t). What is dydt\dfrac{dy}{dt} at t=2t=2? (a) 6ln⁡77 e(ln⁡7)2\dfrac{6\ln 7}{7}\,e^{(\ln 7)^{2}} (b) 3ln⁡77 e(ln⁡7)2\dfrac{3\ln 7}{7}\,e^{(\ln 7)^{2}} (c) 6ln⁡77 eln⁡7\dfrac{6\ln 7}{7}\,e^{\ln 7} (d) 67 e(ln⁡7)2\dfrac{6}{7}\,e^{(\ln 7)^{2}}

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