if y=cos-1(3+5cosx)/(5+3cosx) find dy/dx - Maths - Continuity and Differentiability

Question

if y=cos-1(3+5cosx)/(5+3cosx) find dy/dx?????

Ajanta Trivedi · Accepted Answer

the given equation is:

$y = \cos^{- 1} (\frac{3 + 5 \cos x}{5 + 3 \cos x}) \Rightarrow \cos y = \frac{3 + 5 \cos x}{5 + 3 \cos x} .............. (1)$

differentiating wrt x on the both sides:

$- \sin y \cdot \frac{d y}{d x} = \frac{(5 + 3 \cos x) (- 5 \sin x) - (3 + 5 \cos x) (- 3 \sin x)}{(5 + 3 \cos x)^{2}} - \sin y \cdot \frac{d y}{d x} = \frac{- \sin x (25 + 15 \cos x - 9 - 15 \cos x)}{(5 + 3 \cos x)^{2}} - \sin y \cdot \frac{d y}{d x} = \frac{- 16 \sin x}{(5 + 3 \cos x)^{2}} \frac{d y}{d x} = 16 \cdot \frac{\sin x}{\sin y} * \frac{1}{(5 + 3 \cos x)^{2}}$

hope this helps you.

cheers!!