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shahzadjalbani

  • 2 years ago

How to derivate logarithmic and exponenetial functions ........?

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  1. mathdood
    • 2 years ago
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    show an example

  2. mathdood
    • 2 years ago
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    ln(x) = 1/x is that what you are looking for?

  3. mathdood
    • 2 years ago
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    I mean the derivative of ln(x) is 1/x or if it were 5ln(x) would be 5/x know what I mean?

  4. maheshmeghwal9
    • 2 years ago
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    \[\color{red}{\frac{d}{dx}e^x=e^x.}\]\[\color{blue}{\frac{d}{dx}a^x=a^x \log_e{a}.} \]\[\color{green}{\frac{d}{dx}\log_e{x}=\frac{1}{x}. }\]

  5. shahzadjalbani
    • 2 years ago
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    Yes of coarse but please discuss more deeply that I understand clearly........... @mathdood

  6. mathdood
    • 2 years ago
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    Okay do you want a proof of d/dx ln(x) = 1/x ?

  7. shahzadjalbani
    • 2 years ago
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    Yes I want proof...... and I will a problem after a short while please solve it as well....

  8. shahzadjalbani
    • 2 years ago
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    @mathdood

  9. mathdood
    • 2 years ago
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    Okay I will try to do the proof just give me a second. This is one of those things you really just memorize though like d/dx sin(x) = cos(x) know what I mean? Anyway I will give it a shot.

  10. mathdood
    • 2 years ago
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    Okay I am using the definition of a derivative to do this you are familiar with that right?

  11. shahzadjalbani
    • 2 years ago
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    (x-2)/ ln(x+2) derivate...

  12. mathdood
    • 2 years ago
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    Wait are you asking me to take the derivative of what you just typed or do you want the proof of ln(x) = 1/x ?

  13. mathdood
    • 2 years ago
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    sorry d/dx ln(x) = 1/x I mean

  14. mathdood
    • 2 years ago
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    Is this what you just type (x-2)/ln(x+2) ? If it is I just do this (x-2)*(ln(x+2))^-1 then use product rule. So (1/(ln(x+2))) + ((-1)(x-2)(1/(x+2))(1/(ln(x+2))^2)).

  15. mathdood
    • 2 years ago
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    Now are you interested in the proof or?

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