Question
Differentiate the $\frac{{{e^x}}}{{\sin x}}$ w.r.t x.
$\therefore \frac{{dy}}{{dx}} = \frac{{\sin x\frac{d}{{dx}}{e^x} - {e^x}\frac{d}{{dx}}\sin x}}{{{{\sin }^2}x}}$ [By quotient rule]
$= \frac{{\sin x.{e^x} - {e^x}\cos x}}{{{{\sin }^2}x}}$
$= {e^x}\frac{{\left( {\sin x - \cos x} \right)}}{{{{\sin }^2}x}}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $X_i$ | $0$ | $1$ | $2$ |
| $P_i$ | $3c^3$ | $4c - 10c^2$ | $5c - 1$ |