Derivative

The graph of \( f \) is given in the figure, where \( A \), \( B \) and \( C \) are points of the graph, and \( y \)-coordinate of the point \( B \) is the minimum value of the function \( f \). If \( x_A \), \( x_B \) and \( x_C \) denote the \( x \)-coordinates of the points \( A \), \( B \) and \( C \), and if \( f' \) is the derivative of \( f \), then:

The graph of \( f \) is given in the figure, where \( A \), \( B \) and \( C \) are points on the graph and \( y \)-coordinate of the point \( B \) is the maximum value of the function \( f \). If \( x_A \), \( x_B \) and \( x_C \) denote the \( x \)-coordinates of the points \( A \), \( B \) and \( C \), and if \( f' \) is the derivative of \( f \), then:

Which of the statements A, B, C, D given bellow are incorrect? \[ \begin{array}{l} \text{A: }\left(\ln\frac x2\right)'=\frac1x,\ x\in\mathbb{R}^+ \\ \text{B: }\left(5\sin⁡3x\right)'=5\cos⁡3x \\ \text{C: }\left(\frac1{\left(x^3-1\right)^2}\right)'=\frac{-6x^2}{\left(x^3-1\right)^3},\ x\in\mathbb{R}\setminus\{1\} \\ \text{D: }\left(\ln⁡(1+\cos⁡ x ) \right)'=\frac1{1-\sin ⁡x},\ x\neq\frac{\pi}2+2k\pi,\ k\in\mathbb{Z} \end{array}\] The only incorrect statements are:

Which of the statements A, B, C given bellow are correct? \[ \begin{array}{l} \text{A: }\left(\frac1{x^3}\cdot\cos ⁡x\right)' =-\frac{\cos x+\sin ⁡x}{x^4},\ x\in\mathbb{R}\setminus\{0\} \\ \text{B: }\bigl(\left(1-x^3\right)\cdot\ln x \bigr)'=-3x^2\ln x+\frac1x - x^2,\ x\in\mathbb{R}^+ \\ \text{C: } \left(5^x\cdot\sqrt[5]x\right)'=5^{x-1}\sqrt[5]x\left(5\ln⁡5+\frac1x\right),\ x\in\mathbb{R}\setminus\{0\} \end{array} \] The only correct statements are: