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

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

Options:

Correct Answer: 1

Solution:

dy/dx = 3e^(3x). At x = 0, dy/dx = 3e^(0) = 3.

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

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.

Differentiation of Exponential Functions – The question tests the ability to differentiate the function y = e^(3x) using the chain rule.
Evaluation of Derivatives – It assesses the skill to evaluate the derivative at a specific point, in this case, x = 0.