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xEnOnn

  • 4 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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  1. .Sam.
    • 4 years ago
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    2^x

  2. arcticf0x
    • 4 years ago
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    Take log on both sides, y=2^x

  3. .Sam.
    • 4 years ago
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    http://www.youtube.com/watch?v=sSE6_fK3mu0

  4. dpaInc
    • 4 years ago
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    \[y=2^{x}\] \[lny=xln2\] \[[lny]\prime=\ln2\] \[y'/y=\ln2\] \[y'=\ln2*y'\] \[y'=2^{x}*\ln2\]

  5. .Sam.
    • 4 years ago
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    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

  6. xEnOnn
    • 4 years ago
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    ohh...Thank you!!!

  7. dpaInc
    • 4 years ago
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    sorry, second to the last line should read y' = ln2 * y

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