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What will be the differential function of √(x^2 + 2)?(a) x√(x^2 + 2) dx(b) x/√(x^2 + 2) dx(c) x/√(x^2 – 2) dx(d) -x/√(x^2 + 2) dxThe question was posed to me during an online exam.I want to ask this question from Application of Derivative topic in section Application of Derivatives of Mathematics – Class 12

Answer»

Right option is (B) X/√(x^2 + 2) dx

To elaborate: Let, y = f(x) = √(x^2 + 2)

So, f(x) = (x^2 + 2)^1/2

On DIFFERENTIATING it we get,

f’(x) = d/dx[(x^2 + 2)^1/2]

f’(x) = 1/2 * 1/√(x^2 + 2) * 2x

So f’(x) = x/√(x^2 + 2)

So the differential EQUATION is:

DY = f’(x)dx

Hence, dy = x/√(x^2 + 2) dx


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