Question

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) dx

This 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 1

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