Let . Which of the following expressions is equal to…

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

Problem

Let g(x)=ln⁡(4x2+1)e5xg(x)=\dfrac{\ln(4x^{2}+1)}{e^{5x}}. Which of the following expressions is equal to g′(x)g'(x)? (a) e−5x(8x4x2+1+5ln⁡(4x2+1))e^{-5x}\left(\dfrac{8x}{4x^{2}+1}+5\ln(4x^{2}+1)\right) (b) e−5x(8x4x2+1−5ln⁡(4x2+1))e^{-5x}\left(\dfrac{8x}{4x^{2}+1}-5\ln(4x^{2}+1)\right) (c) e5x(8x4x2+1−5ln⁡(4x2+1))e^{5x}\left(\dfrac{8x}{4x^{2}+1}-5\ln(4x^{2}+1)\right) (d) e−5x(84x2+1−5ln⁡(4x2+1))e^{-5x}\left(\dfrac{8}{4x^{2}+1}-5\ln(4x^{2}+1)\right)

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