Which of the following expressions equals the derivative of for ?

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

Problem

Which of the following expressions equals the derivative of g(x)=ln⁡x e2xg(x)=\ln x\,e^{2x} for x>0x>0? (a) e2x(1x+ln⁡x)e^{2x}\left(\dfrac{1}{x}+\ln x\right) (b) e2x(1x+2ln⁡x)e^{2x}\left(\dfrac{1}{x}+2\ln x\right) (c) e2x(1x−2ln⁡x)e^{2x}\left(\dfrac{1}{x}-2\ln x\right) (d) e2x(2+ln⁡xx)e^{2x}\left(2+\dfrac{\ln x}{x}\right)

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