Which of the following represents the derivative of f(x) = $$x^3$$ * $$e^x$$ ?

$$x^3$$ * $$e^x$$ + $$3x^2$$ * $$e^x$$

$$x^3$$ * $$e^x$$ - $$3x^2$$ * $$e^x$$

Calculus Mathematics Quiz: Differentiation Problems

Reviewed by Janaisa Harris

Janaisa Harris, BA (Mathematics) |

High School Math Teacher

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Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.

, BA (Mathematics)

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Calculus Mathematics Quiz: Differentiation Problems - Quiz

Are you an expert in Calculus Mathematics? Would you like to try this calculus mathematics quiz: differentiation problems? We have an amazing calculus mathematics quiz for you, in which you can solve the Differentiation problems. You can answer the questions correctly to get your best score. These questions will also hone your math skills even further. So, have fun, check your knowledge and try to get the perfect score on the quiz.

Questions and Answers

1.

Differentiate y=2x⁴-4x+5
- A.
  
  8x⁴-4x
- B.
  
  8x³-4
- C.
  
  24x³+4
- D.
  
  8x⁴+4x
- E.
  
  None of the above
Correct Answer
B. 8x³-4

Explanation
The given expression is y=2x^4-4x+5. To differentiate this expression, we need to find the derivative with respect to x. Taking the derivative of each term, we get 8x^3 for the first term, -4 for the second term (as the derivative of -4x is -4), and 0 for the constant term. Therefore, the correct answer is 8x^3-4, which matches the given answer.

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2.

Differentiate of x⁶ is 6x, true or false?
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The statement is false because the given differentiation is incorrect. The correct differentiation of x^6 is 6x^5.

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3.

Differentiate y= -6x⁴+3x²-12x
- A.
  
  24x³-6x
- B.
  
  -24x⁵+3x²-12x
- C.
  
  -24x³+6x-12
- D.
  
  64x³-6x
Correct Answer
C. -24x³+6x-12

Explanation
The given expression y = -6x^4 + 3x^2 - 12x can be differentiated using the power rule of differentiation. The power rule states that for a term of the form ax^n, the derivative is given by nax^(n-1). Applying this rule to each term in the expression, we get the derivative as -24x^3 + 6x - 12.

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4.

Differentiate y=7x²- 3e^3x+1
- A.
  
  14 - 9e^3x+1
- B.
  
  14x²-3e^4x+1
- C.
  
  14x - 3e
- D.
  
  14x - 9e^3x+1
- E.
  
  None of the above
Correct Answer
D. 14x - 9e^3x+1

Explanation
The given answer, 14x - 9e3x+1, is the correct differentiation of the function y=7x2 - 3e3x+1. The derivative of 7x2 is 14x, and the derivative of -3e3x+1 is -9e3x+1. Therefore, the correct answer is 14x - 9e3x+1.

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5.

Differentiate of y= 3e^-3x is -9e^-3x true or false?
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The given statement is true. The correct differentiation of y= 3e-3x is -9e-3x. This can be obtained by applying the power rule of differentiation, which states that the derivative of e^kx is k * e^kx. In this case, k is -3x, so the derivative becomes -3 * e^-3x. Simplifying further, we get -9e^-3x, which matches the given answer. Therefore, the statement is true.

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11
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6.

Differentiate y= tan (3x²-1)
- A.
  
  Sec²(3x²-1)
- B.
  
  6x sec² (3x²-1)
- C.
  
  3x sec² (3x²-10
- D.
  
  Sec² (3x-1)
Correct Answer
B. 6x sec² (3x²-1)

Explanation
The correct answer is 6x sec^2(3x^2-1). To differentiate y = tan(3x^2-1), we can use the chain rule. The derivative of tan(u) is sec^2(u), and the derivative of (3x^2-1) with respect to x is 6x. Therefore, the derivative of y = tan(3x^2-1) is 6x sec^2(3x^2-1).

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7.

Which of the following represents the derivative of f(x) = x^3 * e^x ?
- A.
  
  3x^2 * e^x
- B.
  
  X^3 * e^x + 3x^2 * e^x
- C.
  
  X^3 * e^x - 3x^2 * e^x
- D.
  
  E^x
Correct Answer
B. X^3 * e^x + 3x^2 * e^x
8.

Differentiate y = x(3x²- 5)
- A.
  
  9x² -5x
- B.
  
  9x - 5
- C.
  
  6x
- D.
  
  9x² - 5
- E.
  
  None of the above
Correct Answer
D. 9x² - 5

Explanation
The correct answer is 9x^2 - 5. This is the correct answer because when we differentiate the given function, we use the power rule of differentiation. The power rule states that when differentiating a function of the form x^n, the derivative is nx^(n-1). Applying this rule to the given function, we differentiate the term 3x^2 to get 6x, and the constant term -5 differentiates to 0. Therefore, the derivative of y = x(3x^2 - 5) is 3x^2 + 6x - 5. Simplifying this expression gives us the correct answer of 9x^2 - 5.

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Janaisa Harris |BA (Mathematics) |

High School Math Teacher

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Dec 29, 2020

Quiz Created by
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Calculus Mathematics Quiz: Differentiation Problems

Differentiate y=2x4-4x+5

Differentiate of x6 is 6x, true or false?

Differentiate y= -6x4+3x2-12x

Differentiate y=7x2 - 3e3x+1

Differentiate of y= 3e-3x is -9e-3x true or false?

Differentiate y= tan (3x2-1)

Which of the following represents the derivative of f(x) = x^3 * e^x ?

Differentiate y = x(3x2 - 5)

Differentiate y=2x⁴-4x+5

Differentiate of x⁶ is 6x, true or false?

Differentiate y= -6x⁴+3x²-12x

Differentiate y=7x²- 3e^3x+1

Differentiate of y= 3e^-3x is -9e^-3x true or false?

Differentiate y= tan (3x²-1)

Differentiate y = x(3x²- 5)