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If y = e^(3x), find dy/dx at x = 0.

Practice Questions

Q1
If y = e^(3x), find dy/dx at x = 0.
  1. 1
  2. 3
  3. e
  4. 3e

Questions & Step-by-Step Solutions

If y = e^(3x), find dy/dx at x = 0.
Correct Answer: 3
  • Step 1: Identify the function given in the question. Here, the function is y = e^(3x).
  • Step 2: To find dy/dx, we need to differentiate the function y = e^(3x) with respect to x.
  • Step 3: Use the chain rule for differentiation. The derivative of e^(u) is e^(u) * du/dx, where u = 3x.
  • Step 4: Calculate du/dx. Since u = 3x, then du/dx = 3.
  • Step 5: Now apply the chain rule: dy/dx = e^(3x) * 3 = 3e^(3x).
  • Step 6: Next, we need to find dy/dx at x = 0. Substitute x = 0 into the derivative we found.
  • Step 7: Calculate dy/dx at x = 0: dy/dx = 3e^(3*0) = 3e^(0).
  • Step 8: Since e^(0) = 1, we have dy/dx = 3 * 1 = 3.
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