Question:
If \(u=\sin^{-1}(\frac{2x}{1+x^2})\) and \(v=\tan^{-1}(\frac{2x}{1-x^2})\) then \(\frac{du}{dv}\) is
If \(u=\sin^{-1}(\frac{2x}{1+x^2})\) and \(v=\tan^{-1}(\frac{2x}{1-x^2})\) then \(\frac{du}{dv}\) is
Updated On: Apr 17, 2024
- \(\frac{1-x^2}{1+x^2}\)
- \(\frac{1}{2}\)
- 1
- 2
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct answer is (C) : 1.
Was this answer helpful?
1
0
Top Questions on Derivatives
- Match List-I with List-II:
List-I List-II The derivative of \( \log_e x \) with respect to \( \frac{1}{x} \) at \( x = 5 \) is (I) -5 If \( x^3 + x^2y + xy^2 - 21x = 0 \), then \( \frac{dy}{dx} \) at \( (1, 1) \) is (II) -6 If \( f(x) = x^3 \log_e \frac{1}{x} \), then \( f'(1) + f''(1) \) is (III) 5 If \( y = f(x^2) \) and \( f'(x) = e^{\sqrt{x}} \), then \( \frac{dy}{dx} \) at \( x = 0 \) is (IV) 0 Choose the correct answer from the options given below :- CUET (UG) - 2024
- Mathematics
- Derivatives
- Let f: R → R be the function \(f(x) = \frac{1}{1+e^{-x}}\)
The value of the derivative of ƒ at x where f(x) = 0.4 is ______
(rounded off to two decimal places).
Note: R denotes the set of real numbers. - Match List-I with List-II:
List-I (Function) List-II (Derivative w.r.t. x) (A) \( \frac{5^x}{\ln 5} \) (I) \(5^x (\ln 5)^2\) (B) \(\ln 5\) (II) \(5^x \ln 5\) (C) \(5^x \ln 5\) (III) \(5^x\) (D) \(5^x\) (IV) 0
Choose the correct answer from the options given below.- CUET (UG) - 2024
- Mathematics
- Derivatives
- \(\text{ If } \sin y = x \sin(a + y), \text{ then } \frac{dy}{dx} \text{ is:}\)
- CUET (UG) - 2024
- Mathematics
- Derivatives
- If \(n-1C_r= (k^2-8)^nC_r+1\) Find \(k\).
- JEE Main - 2024
- Mathematics
- Derivatives
View More Questions
Questions Asked in KCET exam
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
- A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is
- KCET - 2023
- Quantum Physics
View More Questions