If $x^m + y^m = k, (m \neq 1)$ and $y'' = \dfrac{ax^b}{y^c}$ such that $a + b + c = 0$, then the value of k is...

If $y = \sin^{-1}\left(\dfrac{25 - x^2}{25 + x^2}\right)$, then $y'(1)$ is...

If $f(x)$ and $g(x)$ are inverse functions of each other and $f(x) = x + e^x$, then $g'(x) = $...

If $3y^2 - 2xy - x = 0$, then the value of $\dfrac{dy}{dx}$ at $y = 2$ is...