Step 1: Identify the function. We have y = e^(3x).
Step 2: Recognize that we need to find the derivative of y with respect to x, which is dy/dx.
Step 3: Use the chain rule. The chain rule states that if you have a function of a function, you take the derivative of the outer function and multiply it by the derivative of the inner function.
Step 4: The outer function is e^(u) where u = 3x. The derivative of e^(u) with respect to u is e^(u).
Step 5: Now find the derivative of the inner function u = 3x. The derivative of 3x with respect to x is 3.
Step 6: Combine the results from Step 4 and Step 5. We have dy/dx = e^(3x) * 3.
Step 7: Simplify the expression. This gives us dy/dx = 3e^(3x).
Exponential Functions – Understanding the properties of exponential functions and their derivatives.
Chain Rule – Applying the chain rule for differentiation when dealing with composite functions.
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