Derivative

1003112007

Level: 
A
Which of the statements A, B, C, D given bellow are correct? \[ \begin{array}{l} \text{A: }\ \left(3x^3-5x^2+7x\right)'=9x^2-10x+7\text{, }x\in\mathbb{R} \\ \text{B: }\ \left(x^2+2x^{-2}-5\right)'=2x-4x^{-3}\text{, }x\in\mathbb{R}\setminus\{0\} \\ \text{C: }\ \left(5x^4-7x^3+2\pi\right)'=20x^3-21x^2+2\text{, }x\in\mathbb{R} \\ \text{D: }\ \left(x^4-\frac4{x^4}\right)'=4x^3-\frac{16}{x^3}\text{, }x\in\mathbb{R}\setminus\{0\} \end{array} \] The only correct statements are:
A, B
A, C
A, B, C
A, D
A, C, D

1003112009

Level: 
A
Which of the statements A, B, C, D given bellow are incorrect? \[ \begin{array}{l} \text{A: }\ \left(\sqrt{x}-\cos⁡ x+\mathrm{ln}\, ⁡x\right)'=\frac1{2\sqrt x}+\sin x+\frac1x\text{, }x\in\mathbb{R}^+ \\ \text{B: }\ \left(3\sin x-3^x+x^3 \right)'=3\cos x-3^x+3x^2 \text{, }x\in\mathbb{R} \\ \text{C: }\ \left(\mathrm{cotg}\, x-\mathrm{log}_3 5\right)'=-\frac1{\sin^2 x}\text{, }x\in\mathbb{R}\setminus\bigcup\limits_{k\in\mathbb{Z}}\{k\pi\} \\ \text{D: }\ \left(3\sqrt[3]{x^2}-2\mathrm{e}^x \right)'=\frac2{\sqrt[3]x}-2\mathrm{e}^x\text{, }x\in\mathbb{R}\setminus\{0\} \end{array} \] The only incorrect statements are:
B
B, C
A, B, C
C, D
B, C, D
C