Continuity and ...

$$\displaystyle \frac{d}{dx}\left ( x^{\log x} \right )$$ is equal to

If $$\displaystyle y= \frac {\sqrt[3]{1+3x}\sqrt[4]{1+4x}\sqrt[5]{1+5x}}{\sqrt[7]{1+7x}\sqrt[8]{1+8x}}$$, then $$y'(0)$$ is equal to

Find $$ \displaystyle  \frac{dy}{dx}$$ if $$ y=x^{x} $$

 Find $$ \displaystyle \frac { dy }{ dx }$$ at $$t =\displaystyle \frac { \pi  }{ 4 }$$ if $$y =\displaystyle  \cos ^{ 4 }{ t } $$  & $$x =\displaystyle \sin ^{ 4 }{ t } $$.

Derivative of sin x w.r.t. cos x is

If $$y=\tan ^{ -1 }{ \sqrt { \dfrac { 1-\sin { x }  }{ 1+\sin { x }  }  }  } $$, then the value of $$\dfrac { dy }{ dx } $$ at $$x=\dfrac { \pi  }{ 6 } $$ is

If $$x=a\, cos^3\theta$$ and $$y=a\, sin^3\theta$$, then $$\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}$$ is equal to

The function represented by  the following graph is.

If $$x = ct$$ and $$y = \dfrac {c}{t}$$, find $$\dfrac {dy}{dx}$$ at $$t = 2$$

If y = cos t and x = sin t, then what is $$\dfrac{dy}{dx}$$ equal to ?