Need advice

>>8799185
I would also have given you 0 points for that but for different reasons.

>>8799205
Why would you give me a zero? Explain your reasons

>>8799185

Your answer doesn't make any sense. You showed an identity, then integrated something that was not even what you had. I would have also given you a flat 0. There is nothing logical in what you did

Just use quotient rule on 1/cosh(x). And you messed up the u substitution anyway, it should be -1/u^2 inside the integral.

>>8799233
rewrite -sechxtanhx as sinhx/(coshx)^2
Then integrate that.
How is what I did illogical?

>>8799210
No words between the equations saying how they relate to each other or which theorems you use. Not writing why [math]u^{-1} = \text{sech } x[/math] implies that [math] \dfrac{d}{dx} \text{sech } x = -\text{sech } x \tanh x [/math].

Several errors in the equations like
[math]\int - \frac{ \sinh x}{ \cosh^2 x} [/math] instead of [math]\int - \frac{ \sinh x}{ \cosh^2 x} dx [/math]
[math] u = \cosh [/math] instead of [math] u = \cosh x [/math]
[math] du = -\sinh [/math] instead of [math] du = - \sinh x dx [/math]
and most importantly no [math]+C [/math] after indefinite integration.

>>8799251
So basically notation, the one thing that doesn't define understanding.

Thanks

If I were your prof I'd fail you on your hand writing alone

>>8799185
>I got the question completely wrong because I didn't do it by deriving.
No, you got the question wrong because your work is completely fucking illegible, contains errors that happen to cancel each other (you did the substitution wrong despite literally being given the derivative of cosh in the question, and you integrated a basic power function wrong) and there is zero explanation as to what this nonlinear blob of scribblings is trying to do.

it's not some rigid "do it this way or you get zero!!!" Nazi behaviour. If you communicate your solution like a baboon, your TA cannot mark it.

>>8799261
Alright this is a fair answer so I'll just take the grade.

>>8799241
du = -sinhxdx

>>8799185
why the fuck did you integrate on a question that clearly asks you to differentiate?
[math]\frac{d}{dx}(\frac{1}{cosh(x)}) = \frac{0*cosh(x)-1*sinh(x)}{cosh^2(x)}\\
=-\frac{1}{cosh(x)}\cdot\frac{sinh(x)}{cosh(x)}
=-sech(x)tanh(x)[/math]
By integrating you add another step onto your answer as you now need to justify that the arbitrary constant of integration now = 0

What the fuck why integrate and not just use the chain rule? Am I missing something here?

>>8799257

Mathematics is not purely about understanding, it is also about showing to there that your reasoning is rigorous AND comprehensible.

And clearly you DONT understand what's going on because your work makes no fucking sense

>>8799289
it was given that d(cosh x)/dx is sinh x

File: bern.gif (3KB, 583x101px) Image search: [Google]

3KB, 583x101px

>>8799185

>>8799185
I would have given you 0 just for using pen.
Although, it is also ridiculous to not just use the quotient rule for differentiation. In addition, you didn't put in the work to explain that integration is the inverse transformation to differentiation.

>>8800953
The integral of cosine is negative sine anon.

>>8800974
Not op, I only use pen. My tests don't have mistakes though. Pencils promote dishonesty

>>8801639
It also prevents autism.

>>8800975
>that's the biggest mistake in the image