The values of $x$,at which the first derivative of the function $(\sqrt{x} + \frac{1}{\sqrt{x}})^2$ with respect to $x$ is $\frac{3}{4}$,are

Let $3f(x) - 2f(1/x) = x,$ then $f'(2)$ is equal to

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function. We say that $f$ has $PROPERTY \ 1$ if $\lim_{h \rightarrow 0} \frac{f(h)-f(0)}{\sqrt{|h|}}$ exists and is finite,and $PROPERTY \ 2$ if $\lim_{h \rightarrow 0} \frac{f(h)-f(0)}{h^2}$ exists and is finite. Then which of the following options is/are correct?
$(1) \ f(x)=x|x|$ has $PROPERTY \ 2$
$(2) \ f(x)=x^{2/3}$ has $PROPERTY \ 1$
$(3) \ f(x)=\sin x$ has $PROPERTY \ 2$
$(4) \ f(x)=|x|$ has $PROPERTY \ 1$

If $y = \frac{x^4 - x^2 + 1}{x^2 + \sqrt{3}x + 1}$ and $\frac{dy}{dx} = ax + b$,then the value of $a + b$ is equal to

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$,then $g^{\prime}(x)$ is equal to

Differentiate the function with respect to $x$: $\sin^{3} x + \cos^{6} x$