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 2 years ago
Can someone show me the steps to this differentiation? \[\frac { d }{ dx } { 2 }^{ x }\]
How should I start with differentiating this?
 2 years ago
Can someone show me the steps to this differentiation? \[\frac { d }{ dx } { 2 }^{ x }\] How should I start with differentiating this?

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arcticf0x
 2 years ago
Best ResponseYou've already chosen the best response.0Take log on both sides, y=2^x

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1\[y=2^{x}\] \[lny=xln2\] \[[lny]\prime=\ln2\] \[y'/y=\ln2\] \[y'=\ln2*y'\] \[y'=2^{x}*\ln2\]

.Sam.
 2 years ago
Best ResponseYou've already chosen the best response.3d/dx e^x : by d/dx ln(x) Given : d/dx ln(x) = 1/x; Chain Rule; d/dx x = 1. (1) d/dx ln(e^x) = d/dx x = 1 d/dx ln(e^x) = d/du ln(u) d/dx e^x (Set u=e^x) = 1/u d/dx e^x = 1/e^x d/dx e^x = 1 (equation 1) d/dx e^x = e^x

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1sorry, second to the last line should read y' = ln2 * y
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