If $f(x) = \cos x \cos 2x \cos 4x \cos 8x \cos 16x$, then $f'\left(\dfrac{\pi}{4}\right)$ is equal to

The derivative of the function $f(x) = \cos^4 x + \sin^4 x,\ 0 \leq x \leq 2\pi$ is positive for

The tangent to the curve intersects the Y-axis at point P. A line drawn through point P is perpendicular to this tangent and passes through another point $(1, 0)$. The differential equation of the curve is...

The function $f(x) = \int \dfrac{x+3}{x^2-9x+20}\,dx$, then $f(x)$ is