Need advice

I had a calc 2 quiz a few days ago and the first question on the quiz was as follows:

[math]\text{Given that } \dfrac{d}{dx} cosh x = sinh x \text{ and } \dfrac{d}{dx} sinh x = cosh x \text{, } \newline \text{show that } \dfrac{d}{dx} sech x = -sechx \text{ }tanhx[/math]

Pic related is my work so that you can see the situation as unbiased as possible. I basically proved it by taking the integral and doing u subtitution.
I got the question completely wrong because I didn't do it by deriving. Teach said I didn't use the given derivatives of cosh and sinh.
But technically I did when I did the derivative of u. And if you were to do the question by deriving you wouldn't even use the derivative of sinh at all because it would be multiplied by 0.

Should I try to get the grade changed? I asked him about it and he said I lost the points because I didn't derive and I didn't use the given identities.

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

Why would you give me a zero? Explain your reasons

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.

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

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.

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

>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.

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

du = -sinhxdx

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?

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

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

...

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.

The integral of cosine is negative sine user.

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

It also prevents autism.

>that's the biggest mistake in the image