Derivative

2010002006

Level: 
B
Differentiate the following function. \[ f(x) = \frac{2-x^{2} } {4x} \]
\(f'(x) = \frac{-x^{2}-2} {4x^{2}} , \ x\in \mathbb{R} \setminus \{0\}\)
\(f'(x) = \frac{-x} {2} ,\ x\in \mathbb{R} \setminus \{0\}\)
\(f'(x) = \frac{2-x^{2}} {4x^{2}} ,\ x\in \mathbb{R} \setminus \{0\}\)
\(f'(x) = \frac{-x-2} {4x^{2}} ,\ x\in \mathbb{R} \setminus \{0\}\)

2010002005

Level: 
B
Differentiate the following function. \[ f(x)=\cos \left(3-2x^{2} \right) \]
\(f'(x) = 4x\sin \left(3-2x^{2} \right),\ x\in \mathbb{R}\)
\(f'(x) = -4x\sin x,\ x\in \mathbb{R}\)
\(f'(x) = -\sin \left(4x\right),\ x\in \mathbb{R}\)
\(f'(x) = \cos\left(4x+1\right),\ x\in \mathbb{R}\)

2010002004

Level: 
B
Differentiate the following function. \[ f(x) =\cos x(1 -\mathop{\mathrm{cotg}}\nolimits x) \]
\(f'(x) =-\sin x +\cos x + \frac{\cos x} {\sin ^{2}x},\ x\in \mathbb{R}\setminus\{k\pi; k\in \mathbb{Z}\}\)
\(f'(x) = \frac{\cos x} {\sin ^{2}x},\ x\in \mathbb{R}\setminus\{k\pi; k\in \mathbb{Z}\}\)
\(f'(x) =-\sin x +\cos x,\ x\in \mathbb{R}\setminus\{k\pi; k\in \mathbb{Z}\}\)
\(f'(x) =-\sin x +2\cos x,\ x\in \mathbb{R}\setminus\{k\pi; k\in \mathbb{Z}\}\)

2010002003

Level: 
B
Differentiate the following function. \[ f(x) = \mathrm{e}^{x}x^{4} \]
\(f'(x) = \mathrm{e}^{x}x^{3}(x+4),\ x\in \mathbb{R}\)
\(f'(x) = \mathrm{e}^{x}4x^{3},\ x\in \mathbb{R}\)
\(f'(x) = \mathrm{e}^{x}x^{3}(x - 4),\ x\in \mathbb{R}\)
\(f'(x) = \mathrm{e}^{x}x^{3}(x + x\mathrm{e}^{x}),\ x\in \mathbb{R}\)

2010002001

Level: 
A
Differentiate the following function. \[ f(x) = \pi -\frac{\ln 3}{x} \]
\(f'(x) = \frac{\ln 3 }{x^{2}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 0 ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = \ln 3 ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = - \frac{\ln 3}{x^{2}} ;\ x\in \mathbb{R}\setminus \{0\}\)