If \(f\left( 2 \right) =4\ and f^{ ' }\left( 2 \right) =1, \) then find \(\lim _{ x\rightarrow 2 }{ \frac { xf\left( 2 \right) -(2)f\left( x \right) }{ x } }\)

If \(y=\sqrt { \frac { 1+{ e }^{ x } }{ 1-{ e }^{ x } } } \) , show that \(\frac { dy }{ dx } =\frac { { e }^{ x } }{ (1-{ e }^{ x })\sqrt { 1-{ e }^{ 2x } } } \)

If \(\log { ({ x }^{ 2 }+{ y }^{ 2 }) } =2\tan ^{ -1 }{ \frac { y }{ x } , } \) Show that \(\frac { dy }{ dx } =\frac { x+y }{ x-y } .\)

Differentiate x^x with respect to x log x

\(If\quad x=4{ z }^{ 2 }+5,y=6{ z }^{ 2 }+7z+3,\quad find\quad \frac { d^{ 2 }y }{ dx^{ 2 } } \)