Let $f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$,where $x \in R$. Then $f'(10)$ is equal to:

If $f(x) = e^{x} g(x)$,$g(0) = 2$,and $g^{\prime}(0) = 1$,then $f^{\prime}(0)$ is

If $y = \sin (\sqrt {\sin x + \cos x} )$,then $\frac{dy}{dx} = $

If $f(t) = \frac{t}{2} + \frac{1}{4} \log(2t - 1)$,then $f^{\prime}\left(\frac{t+1}{2t+1}\right) = $

Consider the function $f: [1.2, 1.9] \rightarrow \mathbb{R}$ defined by $f(x) = [x]$,where $[x]$ denotes the greatest integer less than or equal to $x$. Which of the following is true?

Let $f$ and $g$ be differentiable functions on $R$ such that $f \circ g$ is the identity function. If for some $a, b \in R$,$g^{\prime}(a) = 5$ and $g(a) = b$,then $f^{\prime}(b)$ is equal to