If $5 f(x) + 3 f\left(\frac{1}{x}\right) = x + 2$ and $y = x f(x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to

If $g(x) = [f(2f(x) + 2)]^2$ and $f(0) = -1, f'(0) = 1$,then $g'(0)$ is

Cosine of the angle of intersection of curves $y = 3^{x - 1} \log x$ and $y = x^x - 1$ is

If $\frac{d}{dx} \left( \frac{x^4 + x^2 + 1}{x^2 + x + 1} \right) = ax + b$,then $a - b =$

If $y = x \left[ \left( \cos \frac{x}{2} + \sin \frac{x}{2} \right) \left( \cos \frac{x}{2} - \sin \frac{x}{2} \right) + \sin x \right] + \frac{1}{2\sqrt{x}}$,then $\frac{dy}{dx} = $

Find the derivative of the following function: $\frac{4x + 5 \sin x}{3x + 7 \cos x}$