What is the derivative of $f (x) = e^{- 6 x} + e$ $f(x)=e^(-6x)+e$ ?

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Answer 1 · 2018-03-13T21:31:37

$- 6 e^{- 6 x}$ $-6e^(-6x)$

We can use the Chain Rule to differentiate this:

Re-write $e^{- 6 x}$ $e^(-6x)$ as ${(e^{x})}^{- 6}$ $(e^x)^(-6)$

Using the chain rule:

$- 6 {(e^{x})}^{- 7} \cdot e^{x} + 0$ $-6(e^x)^(-7)*e^x+0$

$- 6 e^{- 7 x + x} = - 6 e^{- 6 x}$ $-6e^(-7x+x)=-6e^(-6x)$

Note the last term $e$ $e$ is a constant.

What is the derivative of f(x)=e^(-6x)+ef(x)=e−6x+ef(x)=e^(-6x)+e ?