If $${x^2} + {y^2} = 1$$ then

If $$y = {\left( {\sin x} \right)^{\tan x}},$$ then $${{dy} \over {dx}}$$ is equal to

Let $$f(x)$$ be a quadratic expression which is positive for all the real values of $$x$$. If $$g(x)=f(x)+f''(x)$$, then for any real $$x$$,

If $${y^2} = P\left( x \right)$$, a polynomial of degree $$3$$, then $$2{d \over {dx}}\left( {{y^3}{{{d^2}y} \over {d{x^2}}}} \right)$$ equals