Math Problem Statement

theres supposed to be a 2e to the power 3x on your derivative because 6e to the power 3x minus 4e to the power 3x leaves 2e to the power 3x

Solution

Ah, I see! You're absolutely right. If the original expression was something like 6e3x4e3x6e^{3x} - 4e^{3x}, the correct simplification would indeed leave you with:

6e3x4e3x=2e3x6e^{3x} - 4e^{3x} = 2e^{3x}

If you're working with this in the context of derivatives, the derivative of 2e3x2e^{3x} would be:

ddx(2e3x)=23e3x=6e3x\frac{d}{dx}(2e^{3x}) = 2 \cdot 3e^{3x} = 6e^{3x}

This is because of the chain rule, which brings down the exponent as a constant multiplier.

If there was a mistake or confusion in the steps, I hope this clears it up! Let me know if you want to go over this in more detail or have any other questions.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Derivatives
Chain Rule

Formulas

Derivative of e^(ax) = a * e^(ax)

Theorems

Chain Rule

Suitable Grade Level

Grades 11-12