If $xy = c^2$ where $c$ is a constant,then $\frac{dy}{dx}$ is equal to

${d \over {dx}}({x^2}{e^x}\sin x) = $

The side of a square is increasing at the rate of $0.2\,cm/s$. The rate of increase of perimeter with respect to time is $...........\,cm/s$.

If $\angle P - \angle Q = 50^{\circ}$,then find the values of $\angle P$ and $\angle Q$.

Which of the following relation$(s)$ is/are correct?
$(A)\ \sin (90^{\circ}+\theta)=\cos (-\theta)$
$(B)\ \sin (180^{\circ}-\theta)=\cos (90^{\circ}-\theta)$
$(C)\ \sin (360^{\circ}-\theta)=\cos (360^{\circ}-\theta)$
$(D)\ \sin (180^{\circ}+\theta)=\cos (90^{\circ}-\theta)$

If $\tan \theta = \frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant,the value of $\cos \theta$ is: