How do you find the derivative of $e^x * e^(2x) * e^(3x) * e^(4x)$ ?

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Answer 1 · 2016-05-17T08:59:44

$d/dx e^x*e^(2x)*e^(3x)*e^(4x) =10e^(10x)$

Using the property that $a^x*a^y = a^(x+y)$ along with that $d/dx e^x=e^x$ and the chain rule, we have

$d/dx e^x*e^(2x)*e^(3x)*e^(4x) = d/dx e^(x+2x+3x+4x)$

$=d/dxe^(10x)$

$=e^(10x)(d/dx10x)$
(Using the chain rule with the functions $e^x$ and $10x$ )

$=10e^(10x)$

How do you find the derivative of e^x * e^(2x) * e^(3x) * e^(4x)e^x * e^(2x) * e^(3x) * e^(4x)?