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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?
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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Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.1@Vocaloid @Rushwr @isaac4321

freckles
 one year ago
Best ResponseYou've already chosen the best response.4yes \[\frac{d}{dx}e^{x}=e^x \text{ and } \int\limits e^x dx=e^x+C\]

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.1So... The intergral of e^kx is equal to e^kx?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0with respect to k or x ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\int\limits_{}^{}e^{kx} dx \\ u=kx \\ du=k dx \\ \int\limits e^{u} \frac{1}{k} du =\frac{1}{k} \int\limits e^{u} du=...\]

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.1With respect of x I think.

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.1What's the derivitave of ln(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[y=\ln(x) \\ e^{y} =x \] you know how to differentiate e^y w.r.t x right?

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.1Ohhhh so would it be 1/x?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\frac{d}{dx}e^x=e^x \\ \frac{d}{dx}e^{u}=u' e^{u} \\ \frac{d}{dx}e^{y}=y'e^{y} \\ y=\ln(x) \text{ is equivalent \to } e^{y}=x \\ \text{ differentiating both sides gives } y'e^{y}=1 \\ y'=\frac{1}{e^y}=\frac{1}{x} \\ \text{ since } e^{y}=x\]

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.1Oh.. Yay thx @freckles helps a lot

freckles
 one year ago
Best ResponseYou've already chosen the best response.4I was just going off by what we had earlier I think the definition of ln(x) is... \[\ln(x)=\int\limits_1^x \frac{1}{t} dt\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4and the you use the fundamental theorem of calculus to find the derivative of ln(x) w.r.t. x
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