Math for fun#4, THIS IS CALCULUS ALREADY!

Math for fun#4 (calc1), THIS IS CALCULUS ALREADY!

Find the derivative of sin^2x/(1+cot(x))+cos^2x/(1+tan(x)),
d/dx(sin^2x/(1+cot(x))+cos^2x/(1+tan(x)),
hard derivative problem,
simplify trig expression,
challenging calculus problem,

blackpenredpen
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[sehjvxk]

You could've also substituted the sin(x)*cos(x) by (0.5)sin(2x) to make things simpler.

[DougCube]

There isn't really much calculus in this problem -- it's almost all trig simplifications. The original expression is just a complicated way to give (-1/2)sin(2x). You didn't have to use the product rule.

[kloake]

Cool video again! But I should try to calculate it on my own before I watch haha

[mokouf]

Alternative: sinxcosx = (sin2x)/2
d/dx (1-(sin2x)/2) = -2cos2x/2 = -cos2x
This is even easier.

[PhilippeFrancais]

Really enjoying your videos! Your teaching style is perfect for this subject. I just completed a Masters in Physics and wish I would have found your channel earlier. It would be perfect if you had a clip-on microphone though - the one you have is a bit quiet.

[Paul-obhy]

i wouldve just done two quotient rules, that took too long

[mr.random]

the function is undefined at x=-pi/4+ 2pi*n. So it's derivative should also not exist. He made a mistake by just cancelling out sinx+cosx, he should have added condition that it is not 0.

[firstnamelastname]

I would’ve just done it with the stuff at the start

[adminguy]

I didn't get the last step, what means by double angle, which leads to cos2x? Thanks.

[tychophotiou]

Why on earth do you have that ridiculous distracting music in the background. Spoils video.