Which of the statements A, B, C given bellow are correct?
\[
\begin{array}{l}
\text{A: }\left(\frac1{x^3}\cdot\cos x\right)' =-\frac{\cos x+\sin x}{x^4},\ x\in\mathbb{R}\setminus\{0\} \\
\text{B: }\bigl(\left(1-x^3\right)\cdot\ln x \bigr)'=-3x^2\ln x+\frac1x - x^2,\ x\in\mathbb{R}^+ \\
\text{C: } \left(5^x\cdot\sqrt[5]x\right)'=5^{x-1}\sqrt[5]x\left(5\ln5+\frac1x\right),\ x\in\mathbb{R}\setminus\{0\}
\end{array}
\]
The only correct statements are:
Which of the statements A, B, C given bellow are correct?
\[
\begin{array}{l}
\text{A: } \left(\frac{2x-1}{2-x}\right)'=\frac{5-4x}{(2-x)^2},\ x\neq2 \\
\text{B: } \left(\frac{\mathrm{e}^x-1}{x}\right)'=\frac{\mathrm{e}^x(x-1)-1}{x^2},\ x\neq0 \\
\text{C: } \left(\frac{\cos x}{1-\sin x}\right)'=\frac1{1-\sin x},\ x\neq\frac{\pi}2+2k\pi,\ k\in\mathbb{Z}
\end{array}\]
The only correct statements are:
Which of the statements A, B, C, D given bellow are incorrect?
\[
\begin{array}{l}
\text{A: }\left(\ln\frac x2\right)'=\frac1x,\ x\in\mathbb{R}^+ \\
\text{B: }\left(5\sin3x\right)'=5\cos3x \\
\text{C: }\left(\frac1{\left(x^3-1\right)^2}\right)'=\frac{-6x^2}{\left(x^3-1\right)^3},\ x\in\mathbb{R}\setminus\{1\} \\
\text{D: }\left(\ln(1+\cos x ) \right)'=\frac1{1-\sin x},\ x\neq\frac{\pi}2+2k\pi,\ k\in\mathbb{Z}
\end{array}\]
The only incorrect statements are: