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What is the derivative of f(x) = x^5 + 2x^3 - x?

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Question: What is the derivative of f(x) = x^5 + 2x^3 - x?

Options:

  1. 5x^4 + 6x^2 - 1
  2. 5x^4 + 6x^3 - 1
  3. 5x^4 + 2x^2 - 1
  4. 5x^4 + 2x^3

Correct Answer: 5x^4 + 6x^2 - 1

Solution: 

The derivative f\'(x) = d/dx(x^5 + 2x^3 - x) = 5x^4 + 6x^2 - 1.

What is the derivative of f(x) = x^5 + 2x^3 - x?

Practice Questions

Q1
What is the derivative of f(x) = x^5 + 2x^3 - x?
  1. 5x^4 + 6x^2 - 1
  2. 5x^4 + 6x^3 - 1
  3. 5x^4 + 2x^2 - 1
  4. 5x^4 + 2x^3

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^5 + 2x^3 - x?
  • Step 1: Identify the function f(x) = x^5 + 2x^3 - x.
  • Step 2: Recall the power rule for derivatives: d/dx(x^n) = n*x^(n-1).
  • Step 3: Apply the power rule to the first term x^5: The derivative is 5*x^(5-1) = 5x^4.
  • Step 4: Apply the power rule to the second term 2x^3: The derivative is 2*3*x^(3-1) = 6x^2.
  • Step 5: Apply the power rule to the third term -x: The derivative is -1 (since -x is the same as -1*x^1, and the derivative is -1*1*x^(1-1) = -1).
  • Step 6: Combine all the derivatives: f'(x) = 5x^4 + 6x^2 - 1.
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