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Plasmataco

  • one year ago

I just gotta make sure of something. The derivative and intergral of e^x is still e^x right?

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  1. Plasmataco
    • one year ago
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    @Vocaloid @Rushwr @isaac4321

  2. freckles
    • one year ago
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    yes \[\frac{d}{dx}e^{x}=e^x \text{ and } \int\limits e^x dx=e^x+C\]

  3. Plasmataco
    • one year ago
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    Oh. Ok :3 thx

  4. Plasmataco
    • one year ago
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    So... The intergral of e^kx is equal to e^kx?

  5. Plasmataco
    • one year ago
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    Or is it different

  6. ganeshie8
    • one year ago
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    with respect to k or x ?

  7. freckles
    • one year ago
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    \[\int\limits_{}^{}e^{kx} dx \\ u=kx \\ du=k dx \\ \int\limits e^{u} \frac{1}{k} du =\frac{1}{k} \int\limits e^{u} du=...\]

  8. Plasmataco
    • one year ago
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    With respect of x I think.

  9. Plasmataco
    • one year ago
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    One more :3

  10. Plasmataco
    • one year ago
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    What's the derivitave of ln(x)

  11. freckles
    • one year ago
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    \[y=\ln(x) \\ e^{y} =x \] you know how to differentiate e^y w.r.t x right?

  12. Plasmataco
    • one year ago
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    No

  13. freckles
    • one year ago
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    apply chain rule

  14. Plasmataco
    • one year ago
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    Ok...

  15. Plasmataco
    • one year ago
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    Ohhhh so would it be 1/x?

  16. freckles
    • one year ago
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    \[\frac{d}{dx}e^x=e^x \\ \frac{d}{dx}e^{u}=u' e^{u} \\ \frac{d}{dx}e^{y}=y'e^{y} \\ y=\ln(x) \text{ is equivalent \to } e^{y}=x \\ \text{ differentiating both sides gives } y'e^{y}=1 \\ y'=\frac{1}{e^y}=\frac{1}{x} \\ \text{ since } e^{y}=x\]

  17. Plasmataco
    • one year ago
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    Or not...?

  18. freckles
    • one year ago
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    you are right

  19. Plasmataco
    • one year ago
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    Oh.. Yay thx @freckles helps a lot

  20. freckles
    • one year ago
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    I was just going off by what we had earlier I think the definition of ln(x) is... \[\ln(x)=\int\limits_1^x \frac{1}{t} dt\]

  21. freckles
    • one year ago
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    and the you use the fundamental theorem of calculus to find the derivative of ln(x) w.r.t. x

  22. freckles
    • one year ago
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    where x>0

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