Q111 / 160 · TS EAMCET 2006 · Mathematics

If $f(x, y)=\frac{\cos (x-4 y)}{\cos (x+4 y)}$, then $\left.\frac{\partial f}{\partial x}\right|_{y=\frac{x}{2}}$ is equal to :

  • A
    -1
  • Correct answer
    B
    0
  • C
    1
  • D
    2

Solution

$\because \quad f(x, y)=\frac{\cos (x-4 y)}{\cos (x+4 y)}$ $\therefore \quad f\left(x, \frac{\pi}{2}\right)=\frac{\cos (x-2 \pi)}{\cos (x+2 \pi)}$ $=\frac{\cos (2 \pi-x)}{\cos (2 \pi+x)}=\frac{\cos x}{\cos x}=1$ $\therefore \quad \frac{\partial f}{\partial x}=0$

Hence, the correct answer is option: 'B'.

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