Exams › JEE Main › Maths

The derivative of tan⁻¹ ((√(1+x²)-1)/(x)) with respect to tan⁻¹ ((2x√(1-x²))/(1-2x²)) at x=(1)/(2) is:

1. (√(3))/(12)
2. (√(3))/(10)
3. (2√(3))/(5)
4. (2√(3))/(3)

Correct answer: (√(3))/(10)

Solution

The correct option is derived from applying the chain rule and implicit differentiation to the given functions, leading to a simplification that evaluates to frac{ ext{sqrt{3}}}{10} at x = (1)/(2). This result reflects the relationship between the derivatives of the two inverse tangent functions.

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 →