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xEnOnn
Can someone show me the steps to this differentiation? \[\frac { d }{ dx } { 2 }^{ x }\] How should I start with differentiating this?
Take log on both sides, y=2^x
\[y=2^{x}\] \[lny=xln2\] \[[lny]\prime=\ln2\] \[y'/y=\ln2\] \[y'=\ln2*y'\] \[y'=2^{x}*\ln2\]
d/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
sorry, second to the last line should read y' = ln2 * y