The derivative of $f(x) = |x^2 - x|$ at $x = 2$ is

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers): $\frac{a+b \sin x}{c+d \cos x}$

If $3 f(x)-2 f\left(\frac{1}{x}\right)=x$,then $f^{\prime}(2)$ is equal to

If $f(x)$ is a polynomial such that $f(x) = [f'(x)]^2$ and $f(2) = 0$, then $f(-2) = \dots$

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

If $f(x)$ has a derivative at $x = a,$ then $\mathop {\lim }\limits_{x \to a} \frac{xf(a) - af(x)}{x - a}$ is equal to