The function $f(x)=\frac{x}{2}+\frac{2}{x}$ has a local minima at $x$ equal to

Given a curve $y=7 x-x^3$ and $x$ increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when $x=5$ is

The derivative of $$x^{2 x}$$ w.r.t. $$x$$ is:

The interval in which the function $$f(x)=2 x^3+9 x^2 +12 x-1$$ is decreasing is :