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]
$= \frac{{\sin x.{e^x} - {e^x}\cos x}}{{{{\sin }^2}x}}$
$= {e^x}\frac{{\left( {\sin x - \cos x} \right)}}{{{{\sin }^2}x}}$
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$\vec{\text{a}}=2\hat {\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}} =4\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}}$