Ok, so now that I’ve offended you – you probably want to leave this page, however, please remember why you got here in the first place. You simply want to add Latex formulas, equations and expressions to your answers so that you can pick up extra “Brainliest” answers and have Brainly.com’s users massaging your ego. Since it most likely is the case, bear with me for one moment and let me explain how you can perform such a feat with a minimum amount of fuss…

Now, I’m assuming you are a Google Chrome user because this post has been written for “Google Chrome Users Only”. If you aren’t a Google Chrome user – then surely you like the sound of my voice, or more specifically my average writing skills – and for that I’ll praise you. It’s not often people spend seconds reading my posts let alone minutes or hours.

Oh, you’re still here? I guess you are a Google Chrome user after all, therefore I’ll hurry up and demonstrate how to add damn Latex code to answers.

You’re probably familiar with the “Chrome Web Store”. If you aren’t, here’s its link: https://chrome.google.com/webstore/category/apps . Now, what you must do when in this store is search for the app “Daum Equation Editor” because this app is spectacular and in a league of its own (the guys who developed this app haven’t paid me to say this). This app will let you produce mathematical formulas, equations and expressions in Latex and copy and paste them into your answer boxes on Brainly.com. Furthermore, you won’t have to produce any Latex code whatsoever to achieve your lifelong ambitions. Life can’t get any better than that can it? …Copying then placing mathematical codes in to answer boxes on Brainly.com.

Assuming you have downloaded this app thanks to this post,  play around with it and explore its degrees of freedom. If the expressions you have produced are satisfying, then copy and paste the relevant Latex code it provides you with (underneath your expressions) in to your beloved answer(s) on Brainly.com. Make sure it sits within the $$…$$ tags which can be produced by clicking on the “paste/edit equation” button that can be found on answer boxes on Brainly’s site.

If you have any questions concerning copying and pasting Latex codes in to your answer boxes, just message me on my Brainly.com profile page or comment on this post.

Bye, bye for now. Have fun answering maths questions. Hehe. 🙂

# How to differentiate y=arccosx

Below I’ll be demonstrating how to differentiate y=arccosx using implicit differentiation…

$y=\arccos { x } \\ \\ \cos { y=x } \\ \\ -\sin { y\cdot \frac { dy }{ dx } } =1\\ \\ \frac { dy }{ dx } =-\frac { 1 }{ \sin { y } }$

But…

$\sin ^{ 2 }{ y+\cos ^{ 2 }{ y=1 } } \\ \\ \sin ^{ 2 }{ y } =1-\cos ^{ 2 }{ y } \\ \\ \sin { y=\sqrt { 1-\cos ^{ 2 }{ y } } }$

Therefore…

$\frac { dy }{ dx } =-\frac { 1 }{ \sqrt { 1-\cos ^{ 2 }{ y } } } \\ \\ \therefore \quad \frac { dy }{ dx } =-\frac { 1 }{ \sqrt { 1-{ x }^{ 2 } } }$

# How to differentiate y=arcsinx

Below I’ll be demonstrating how to differentiate y=arcsinx using implicit differentiation…

$y=\arcsin { x } \\ \\ \sin { y } =x\\ \\ \cos { y } \cdot \frac { dy }{ dx } =1\\ \\ \frac { dy }{ dx } =\frac { 1 }{ \cos { y } }$

But…

$\sin ^{ 2 }{ y+\cos ^{ 2 }{ y } } =1\\ \\ \cos ^{ 2 }{ y=1-\sin ^{ 2 }{ y } } \\ \\ \cos { y=\sqrt { 1-\sin ^{ 2 }{ y } } }$

Therefore:

$\frac { dy }{ dx } =\frac { 1 }{ \sqrt { 1-\sin ^{ 2 }{ y } } } \\ \\ \therefore \quad \frac { dy }{ dx } =\frac { 1 }{ \sqrt { 1-{ x }^{ 2 } } }$

# How to differentiate y=arctanx

Below I’m going to demonstrate how to integrate y=arctanx…

Firstly, we need to know that:

$\sin ^{ 2 }{ y } +\cos ^{ 2 }{ y } =1\\ \\ \frac { \sin ^{ 2 }{ y } }{ \cos ^{ 2 }{ y } } +\frac { \cos ^{ 2 }{ y } }{ \cos ^{ 2 }{ y } } =\frac { 1 }{ \cos ^{ 2 }{ y } } \\ \\ \tan ^{ 2 }{ y } +1=\sec ^{ 2 }{ y }$

We also need to know that:

$x=\tan { y } \\ \\ x=\frac { \sin { y } }{ \cos { y } } \\ \\ x\cdot \cos { y } =\sin { y } \\ \\ \frac { dx }{ dy } \cdot \cos { y } +x\cdot \left( -\sin { y } \right) =\cos { y } \\ \\ \frac { dx }{ dy } \cdot \cos { y } -x\sin { y } =\cos { y } \\ \\ \frac { dx }{ dy } \cdot \cos { y } =\cos { y } +x\sin { y } \\ \\ \frac { dx }{ dy } \cdot \cos { y } =\cos { y } +\frac { \sin ^{ 2 }{ y } }{ \cos { y } } \\ \\ \frac { 1 }{ \cos { y } } \cdot \frac { dx }{ dy } \cdot \cos { y } =\frac { 1 }{ \cos { y } } \left( \cos { y+\frac { \sin ^{ 2 }{ y } }{ \cos { y } } } \right) \\ \\ \frac { dx }{ dy } =1+\tan ^{ 2 }{ y } \\ \\ \therefore \quad \frac { dx }{ dy } =\sec ^{ 2 }{ y }$

And finally:

$\frac { dy }{ dy } \cdot \frac { dy }{ dx } =\frac { dy }{ dx }$

Now, using implicit differentiation:

$y=\arctan { x } \\ \\ \tan { y } =x\\ \\ \sec ^{ 2 }{ y } \cdot \frac { dy }{ dx } =1\\ \\ \frac { dy }{ dx } =\frac { 1 }{ \sec ^{ 2 }{ y } } \\ \\ \frac { dy }{ dx } =\frac { 1 }{ \tan ^{ 2 }{ y+1 } } \\ \\ \therefore \quad \frac { dy }{ dx } =\frac { 1 }{ { x }^{ 2 }+1 }$