Current Events > I just took my Calc 1 midterm this morning

(+) Yeah! (+)

Totally forgot how to get the derivative of e to any exponent besides x

I hope that's not on the mcdonalds app or I'm fucked
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Well, e^2 or e^3 for example is just a constant number... so the derivative is zero
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Man I feel like I never knew how to do that despite doing well in the class and tests. I dunno how I did well at all. Like I know we learned it, but it didnt stick at all.
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Isnt it basically just chain rule?
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PerseusRad posted...

Man I feel like I never knew how to do that despite doing well in the class and tests. I dunno how I did well at all. Like I know we learned it, but it didnt stick at all.

It's because you just memorized stuff.

If you keep going in math and you do proof based classes at some point you just have to start thinking differently
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heh, calc 1
i remember 3 years ago
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frozenshock posted...

Well, e^2 or e^3 for example is just a constant number... so the derivative is zero

I'm mostly thinking in terms of like e^sinx

WaterLink posted...

Isnt it basically just chain rule?

Pretty much. It's a mix of implicit and logarithmic differentiation

y = e^sinx
Ln of both sides gives you ln y = sin x

Derivative of both sides gets you
1/y(dy/dx) = cosx

Move your y (equal to the original equation) to the right side and you get cosx(e^sinx)

Simple shit but I totally blanked on it when it was important
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Here:


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frozenshock posted...

Here:

Whoever made this...is going places lmao
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I just cannot get the concept of logs and natural logs to stick in my head. I always say that I need to just need to go back to study it hard, but I never do.
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frozenshock posted...

Here:

But that's wrong. 1six= 16
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Sexypwnstar posted...

I just cannot get the concept of logs and natural logs to stick in my head. I always say that I need to just need to go back to study it hard, but I never do.

It's a weird concept at first. It clicked with me when I started thinking of it as the inverse of an exponential function, so you can rearrange it into something familiar

I'm still a little foggy on natural log since funny things start happening with e
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(e^x)' = (x')(e'x)
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MarqueeSeries posted...

Totally forgot how to get the derivative of e to any exponent besides x

I hope that's not on the mcdonalds app or I'm fucked

in short: we're fucked and flunked the goddamn test gawd damnit.
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MarqueeSeries posted...

Pretty much. It's a mix of implicit and logarithmic differentiation

y = e^sinx
Ln of both sides gives you ln y = sin x

Derivative of both sides gets you
1/y(dy/dx) = cosx

Move your y (equal to the original equation) to the right side and you get cosx(e^sinx)

Simple s*** but I totally blanked on it when it was important

Wtf?
Just do the chain rule. Inner times outer
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scar the 1 posted...

MarqueeSeries posted...

Pretty much. It's a mix of implicit and logarithmic differentiation

y = e^sinx
Ln of both sides gives you ln y = sin x

Derivative of both sides gets you
1/y(dy/dx) = cosx

Move your y (equal to the original equation) to the right side and you get cosx(e^sinx)

Simple s*** but I totally blanked on it when it was important

Wtf?
Just do the chain rule. Inner times outer

...that works too

I honestly hadn't thought of that

Kinda cool that it works both ways though
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For me, it was y = f(u), u = f(x)

So dy/dx = dy/du * du/dx

Abuse of notation, but a good mnemonic nonetheless
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Get a job
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REMercsChamp posted...

Get a job

With this GPA? Absolutely not
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MarqueeSeries posted...

Totally forgot how to get the derivative of e to any exponent besides x

I hope that's not on the mcdonalds app or I'm fucked

McLaughlin? Lol, I took an exam today as well.

Use the power rule.

e^pie = pie*e^pie-1

PogonaVitticeps posted...

MarqueeSeries posted...

Totally forgot how to get the derivative of e to any exponent besides x

I hope that's not on the mcdonalds app or I'm fucked

McLaughlin? Lol, I took an exam today as well.

Use the power rule.

e^pie = pie*e^pie-1

How do you think you did on yours?

Also power rule doesn't necessarily work when it's a trig function or polynomial in the exponenent of e, otherwise it'd be sinx(e^sinx-1)
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Nice
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MarqueeSeries posted...

PogonaVitticeps posted...

MarqueeSeries posted...

Totally forgot how to get the derivative of e to any exponent besides x

I hope that's not on the mcdonalds app or I'm fucked

McLaughlin? Lol, I took an exam today as well.

Use the power rule.

e^pie = pie*e^pie-1

How do you think you did on yours?

Also power rule doesn't necessarily work when it's a trig function or polynomial in the exponenent of e, otherwise it'd be sinx(e^sinx-1)

I did good aside from some of the trig.

What about the chain rule then?

Overall, derivatives is just a mixture of power rule, chain rule, product rule, quotient rule, trig derivatives/identities etc.

Math is so fascinating
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Yeah someone pointed it out earlier that the chain rule is the easiest way to do e^(any variable or polynomial), but it's also solvable using implicit and logarithmic differentiation
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PogonaVitticeps posted...

What about the chain rule then?

It always works. You can prove this using the definition of the derivative, but it's trivial and left to the reader as an exercise
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