Continuity and Differentiability — Class 12 Maths Solution

Let $y = \cfrac{{{e^x}}}{{\sin x}}$

therefore, $\cfrac{{dy}}{{dx}} = \cfrac{d}{{dx}}\left( {\cfrac{{{e^x}}}{{\sin x}}} \right) = \cfrac{{\sin x\cfrac{d}{{dx}}({e^x}) - {e^x}\cfrac{d}{{dx}}(\sin x)}}{{{{\sin }^2}x}}$

$= \cfrac{{\sin x \cdot {e^x} - {e^x} \cdot \cos x}}{{{{\sin }^2}x}} = \cfrac{{{e^x}(\sin x - \cos x)}}{{{{\sin }^2}x}},x \ne n\pi ,n \in Z$