Question

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

Answer 1

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

Explanation:

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)`