If $\int f'(x) \cdot e^{x^2}\,dx = (x - 1) \cdot e^{x^2} + k$, where $k$ is constant of integration, then $f(x) = \ldots$

Let $y = \sqrt[p]{x^3 y}$. If $\dfrac{dy}{dx} = \dfrac{3}{2}$ when $y = 1$, then the value of $p$ is equal to $\ldots$

If $f'(x) = \sin^2 x$ and $y = f\left(\dfrac{2x-1}{x^2+1}\right)$, then $\dfrac{dy}{dx}$ at $x = 1$ is

If $f : R \to R$ is an even function then