Question:medium
Let $y = \tan^{-1}\left( \frac{3\cos x - 4\sin x}{4\cos x + 3\sin x} \right) + \tan^{-1}\left( \frac{x}{1 + \sqrt{1 + x^2}} \right)$. Then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$ is :
Let $y = \tan^{-1}\left( \frac{3\cos x - 4\sin x}{4\cos x + 3\sin x} \right) + \tan^{-1}\left( \frac{x}{1 + \sqrt{1 + x^2}} \right)$. Then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$ is :
Updated On: Apr 6, 2026
- $-\frac{5}{7}$
- $\frac{3}{7}$
- $-\frac{3}{2}$
- $\frac{5}{7}$
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Limits
- Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.
- Evaluate \( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \):
The area of the region \( \{(x, y): 0 \leq y \leq x^2 + 1, \, 0 \leq y \leq x + 1, \, 0 \leq x \leq 2\ \) is:}
- The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
- Want to practice more? Try solving extra ecology questions todayView All Questions
