What is the derivative of $x (6^{- 2 x})$ $x(6^(-2x))$ ?

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Answer 1 · 2017-04-13T01:51:26

$= (1 - 2 x ln 6) 6^{- 2 x}$ $=(1-2xln 6)6^(-2x)$

$(x cdot 6^(-2x))'$

$=1 cdot 6^(-2x)+x cdot (6^(-2x))'$

By $(b^x)'=(ln b)b^x$ and Chain Rule,

$=6^(-2x)+x cdot (ln 6)6^(-2x)(-2)$

By factoring out $6^(-2x)$ ,

$=(1-2xln 6)6^(-2x)$

I hope that this was clear.

What is the derivative of x(6^(-2x))x(6−2x)x(6^(-2x))?