$\frac{d}{dx}(\sin 2x^2)$ equals

Let $f(x)=\sin x, g(x)=\cos x, h(x)=x^2$, then $\lim _{x \rightarrow 1} \frac{f(g(h(x)))-f(g(h(1)))}{x-1}=$

Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y) = f(x) + f(y) + xy^2 + x^2y$ for all real $x$ and $y$. If $\lim_{x \rightarrow 0} \frac{f(x)}{x} = 1$,then $f'(3)$ is equal to:

The graph of function $f$ contains the points $P(1, 2)$ and $Q(s, r)$. The equation of the secant line through $P$ and $Q$ is $y = \left( \frac{s^2 + 2s - 3}{s - 1} \right) x - 1 - s$. The value of $f'(1)$ is:

If $r = [2\phi + \cos^2(2\phi + \pi/4)]^{1/2}$,then what is the value of the derivative $dr/d\phi$ at $\phi = \pi/4$?

Cosine of the angle of intersection of curves $y = 3^{x - 1} \log x$ and $y = x^x - 1$ is