$\mathop {\text{Limit}}\limits_{h \to 0} \frac{{\int\limits_a^{x + h} {\ln^2 t \, dt} - \int\limits_a^x {\ln^2 t \, dt} }}{h} = $

If $f: R \rightarrow R$ is an even function having derivatives of all orders, then which of the following is an odd function?

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): $\frac{\sin (x+a)}{\cos x}$

If $f(x) = \sqrt{1 + \cos^2(x^2)}$,then $f'\left(\frac{\sqrt{\pi}}{2}\right)$ is

If $f^{\prime}(x)=a \cos x+b \sin x$ and $f^{\prime}(0)=4, f(0)=3, f\left(\frac{\pi}{2}\right)=5$,then $f(x)=$

Let $f$ and $g$ be differentiable functions satisfying $g'(a) = 2$,$g(a) = b$,and $f \circ g = I$ (identity function). Then $f'(b)$ is equal to