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Questions and Answers
Which of the following is the correct derivative of the function $f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 1$?
Which of the following is the correct derivative of the function $f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 1$?
- $f'(x) = 12x^3 - 6x^2 + 5x + 1$
- $f'(x) = 12x^3 - 6x^2 + 10x - 7$ (correct)
- $f'(x) = 12x^3 - 6x^2 + 10x + 1$
- $f'(x) = 12x^3 - 6x^2 + 5x - 7$
What is the derivative of the function $f(x) = \sqrt{x^2 + 1}$?
What is the derivative of the function $f(x) = \sqrt{x^2 + 1}$?
- $f'(x) = \frac{x},{\sqrt{x^2 + 1}}$
- $f'(x) = \frac{2x},{\sqrt{x^2 + 1}}$ (correct)
- $f'(x) = \frac{1},{\sqrt{x^2 + 1}}$
- $f'(x) = \frac{x^2},{\sqrt{x^2 + 1}}$
What is the derivative of the function $f(x) = e^{3x} \cdot \ln(x)$?
What is the derivative of the function $f(x) = e^{3x} \cdot \ln(x)$?
- $f'(x) = 3e^{3x} \cdot \ln(x)$
- $f'(x) = e^{3x} \cdot \ln(x) + \frac{e^{3x}},{x}$
- $f'(x) = e^{3x} \cdot \ln(x) + \frac{3e^{3x}},{x}$ (correct)
- $f'(x) = 3e^{3x} \cdot \ln(x) + \frac{e^{3x}},{x}$
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