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What will be the differential function of log(x^2 + 4)?(a) 2x/(x^2 + 4) dx(b) 2x/(x^2 – 4) dx(c) -2x/(x^2 + 4) dx(d) -2x/(x^2 – 4) dxThis question was posed to me in an international level competition.The doubt is from Application of Derivative in chapter Application of Derivatives of Mathematics – Class 12

Answer»

Right option is (a) 2x/(x^2 + 4) dx

For EXPLANATION I would say: Let, y = f(x) = LOG(x^2 + 4)

So f(x) = log(x^2 + 4)

On DIFFERENTIATING it we get,

f’(x) = d/dx[log(x^2 + 4)]

So f’(x) = 2x/(x^2 + 4)

So the differential equation is:

DY = f’(x)dx

Hence, dy = 2x/(x^2 + 4) dx


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