Question

If $f(x)=\tan^{-1}\left(\frac{3\cos x-5\sin x}{5\cos x+3\sin x}\right)$ , then the value $f^{\prime}(1)$ is

• A. 1
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. -1
• E. $-\frac{1}{4}$

Hint:

Logic Tip: The derivative of $y = \tan^{-1}\left(\frac{a\cos x - b\sin x}{b\cos x + a\sin x}\right)$ is always exactly $-1$, regardless of what constants $a$ and $b$ are, because it always simplifies to a constant minus $x$.

Answer 1

The Correct Option is D