Exams › JEE Main › Maths

Find the differential coefficient of tan⁻¹(2x/(1-x²)) with respect to sin⁻¹(2x/(1+x²)).

1. 1
2. -1
3. -1/2
4. x

Correct answer: 1

Solution

tan^-1(2x/(1-x^2)) = 2 arctan x and sin^-1(2x/(1+x^2)) = 2 arctan x for |x|<1, so each differentiates to 2/(1+x^2). The required derivative is their ratio, which is 1.

Related JEE Main Maths questions

• For the function f(x) = log(x + √(x² + 1)), which of the following describes it correctly?
• For the function f(x) = log((1 + x)/(1 − x)), which of the following relations is satisfied?
• Find the domain of the function f(x)=sin⁻¹{log2(1/2 x²)}.
• For which values of x does the inequality sin⁻¹(sin 5) > x² − 4x hold?
• Determine the range of the function f(x) = sin⁻¹x + tan⁻¹x + sec⁻¹x.
• If A = tan⁻¹ ((x√(3))/(2K-x)) and B = tan⁻¹ ((2x-K)/(K√(3))), then what is the value of A - B?

⚔️ Practice JEE Main Maths free + battle 1v1 →