Question

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) dx

The 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 1

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