Continuity and ...

If $$y=x^{\left(x^{ x}\right)}$$, then $$\displaystyle\frac{dy}{dx}$$ is

If $$f(x)={|x|}^{|\sin{x}|}$$, then $$\displaystyle f^\prime\left(-\frac{\pi}{4}\right)=$$

If $$x=\sin^{-1}t$$ and $$y=\log(1-{t}^{2})$$ , then $$\displaystyle \left .\frac{{d}^{2}y}{{d}{x}^{2}}\right|_{{t}=\frac{1}{2}} = $$

The weight $$W$$ of a certain stock of fish is given by $$W = nw$$, where n is the size of stock and $$w$$ is the average weight of a fish. If $$n$$ and $$w$$ change with time $$t$$ as $$n = 2t^2 + 3$$ and $$w = t^2 - t + 2$$, then the rate of change of $$W$$ with respect to $$t$$ at $$t = 1$$ is.

$$\displaystyle y=\left ( 1+\frac{1}{x} \right )^{x}+x^{1+\frac{1}{x}}.$$
Differentiate

If $$x=\sin t$$, $$y=\sin kt$$ then value of $$\left ( 1-x^{2} \right )y_{2}-xy_{1}$$ is

If $$f(x)=\left | x \right |+\left | \cos x \right |$$, then

Given the parametric equations $$x=f(t),y=g(t).$$ Then $$\displaystyle \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } $$ equals

Derivative of $${(x\cos{x})}^x$$ with respect to $$x$$ is

If $$x=log(1+t^2)$$ and $$y=t-tan^{-1}t$$. Then, $$\dfrac{dy}{dx}$$ is equal to