1103023902
Level:
A
The figure shows the derivative of one of the functions displayed below. Choose the function.
Derivative
1103023901
Level:
A
The graph of \( f' \) is given in figure. Function \( f' \) is the derivative of a function \( f \). Choose which of the following graphs is the graph of \( f \).
9000070805
Level:
A
Differentiate the following function.
\[
f(x) = -3x^{3} - x^{2} + 9x
\]
\(f'(x) = -9x^{2} - 2x + 9;\ x\in \mathbb{R}\)
\(f'(x) = 9x^{2} - 2x + 9;\ x\in \mathbb{R}\)
\(f'(x) = 27x^{2} - 2x;\ x\in \mathbb{R}\)
\(f'(x) = -9x^{2} - 2x;\ x\in \mathbb{R}\)
9000070807
Level:
B
Differentiate the following function.
\[
f(x) = \frac{x^{4} + 3}
{x^{2}} + x^{3}
\]
\(f'(x) = 3x^{2} + 2x - \frac{6}
{x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 6x^{2} - 2x - \frac{6}
{x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 3x^{2} + 2x + \frac{6}
{x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 6x^{2} - 2x + \frac{6}
{x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
9000070808
Level:
B
Differentiate the following function.
\[
f(x)= \frac{x}
{x + 1}
\]
\(f'(x) = \frac{1}
{(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
\(f'(x) = - \frac{1}
{(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
\(f'(x) = \frac{x}
{(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
\(f'(x) = - \frac{x}
{(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
9000070809
Level:
B
Differentiate the following function.
\[
f(x)= 3x^{2}\sin x
\]
\(f'(x) = 6x\sin x + 3x^{2}\cos x;\ x\in \mathbb{R}\)
\(f'(x) = 6x\cos x;\ x\in \mathbb{R}\)
\(f'(x) = 3x^{2}\sin x\cos x;\ x\in \mathbb{R}\)
\(f'(x) = -3x^{2}\sin x\cos x;\ x\in \mathbb{R}\)
9000070810
Level:
A
Differentiate the following function.
\[
f(x)=\log _{5}12
\]
\(f'(x) = 0;\ x\in \mathbb{R}\)
\(f'(x) = \frac{1}
{\ln 12};\ x\in \mathbb{R}\)
\(f'(x) = \frac{1}
{12\ln 5};\ x\in \mathbb{R}\)
\(f'(x) = 1;\ x\in \mathbb{R}\)
9000070806
Level:
A
Differentiate the following function.
\[
f(x) = \frac{\pi }
{x} +\ln 2
\]
\(f'(x) = - \frac{\pi }{x^{2}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 0;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) =\pi ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = \frac{\pi } {x^{2}} ;\ x\in \mathbb{R}\setminus \{0\}\)
9000070802
Level:
A
Differentiate the following function.
\[
f(x) = 3 - 2\cos x
\]
\(f'(x) = 2\sin x;\ x\in \mathbb{R}\)
\(f'(x) = 3 + 2\sin x;\ x\in \mathbb{R}\)
\(f'(x) = 3 - 2\sin x;\ x\in \mathbb{R}\)
\(f'(x) = 2\cos x;\ x\in \mathbb{R}\)
9000070701
Level:
B
Differentiate the following function.
\[
f(x)= (2x - 5)^{-6}
\]
\(f^{\prime}(x) = - \frac{12}
{(2x-5)^{7}} ;\ x\in \mathbb{R}\setminus \left \{\frac{5}
{2}\right \}\)
\(f^{\prime}(x) = - \frac{12}
{(2x-5)^{7}} ;\ x\in \mathbb{R}\)
\(f^{\prime}(x) = - \frac{12}
{(2x-5)^{5}} ;\ x\in \mathbb{R}\setminus \left \{\frac{5}
{2}\right \}\)
\(f^{\prime}(x) = - \frac{12}
{(2x-5)^{5}} ;\ x\in \left (\frac{5}
{2};\infty \right )\)