# What is the derivative of #e^x * e^(2x) * e^(3x)* e^(4x)#?

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(Or worse yet, I'd use the multiple factor product rule:

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To find the derivative of ( e^x \times e^{2x} \times e^{3x} \times e^{4x} ), you can use the properties of exponents and the chain rule. The derivative of ( e^{ax} ) with respect to ( x ) is ( ae^{ax} ). Applying this rule to each term, the derivative of the given expression is:

[ \frac{d}{dx} \left( e^x \times e^{2x} \times e^{3x} \times e^{4x} \right) = e^x \times 2e^{2x} \times 3e^{3x} \times 4e^{4x} ]

[ = 2 \times 3 \times 4 \times e^{1x + 2x + 3x + 4x} ]

[ = 24e^{10x} ]

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