The area of the square increases at the rate of $0.5 \mathrm{~cm}^2 / \mathrm{sec}$. The rate at which its perimeter is increasing when the side of the square is 10 cm long, is

The equation of normal to the curve $$y=\sin \left(\frac{\pi x}{4}\right)$$ at the point $$(2,5)$$ is

$$\text { If } \sin (x+y)+\cos (x+y)=\sin \left[\cos ^{-1}\left(\frac{1}{3}\right)\right] \text {, then } \frac{dy}{dx}=$$

For every value of $$x$$, the function $$f(x)=\frac{1}{a^x}, a>$$ 0 is,