If $\frac{d}{{dx}}\left[ {\frac{{2{x^3} + 3{x^2} + x - 3}}{{{x^2} + x - 2}}} \right] = A + \frac{B}{{{{(x - 1)}^2}}} + \frac{C}{{{{(x + 2)}^2}}}$ then $(A - B + C)$ is

Let $f: R \to R$ be a function such that $f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$,for all $x \in R$. Then $f(2)$ is equal to

Let $f: R \rightarrow R$ be defined by $f(x) = \log \left[e^x \left(\frac{x-2}{x+2}\right)^{3/4}\right]$. Find the value of $f'(0)$.

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 $f(1)=1$ and $f^{\prime}(1)=3$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

Find the derivative of the function: $4 \sqrt{x} - 2$. (Assume $a, b, c, d, p, q, r, s$ are fixed non-zero constants and $m, n$ are integers.)