So you think you can take the derivative (intro)

3 derivative examples to help you master your differentiation techniques.
How to take the derivative with power rule, product rule, quotient rule, and chain rule. Also, remember to do algebra first before calculus! This will help make the problem easier!

[jonasdaverio]

7:36 "This is a nice one" It's great to see that you have good relationship with the numbers you write. I would be pleased to meet this 1 on the top of the fraction !

[tangentofaj]

To avoid the quotient rule, I would convert to the product rule by rewriting the fractions like sin x / (1 + cos x) as (sin x)*(1+cos x)^-1. That way I could use the chain rule, then use exponents to factor things out and clean everything up. Mostly because I couldn't stand the quotient rule. Absolutely.

[rituchandra]

for the last one sinx/(1+cosx)
write 1+cosx = 2cos^2(x/2)
sinx = 2sin(x/2)cos(x/2)
2sin(x/2)cos(x/2)/2cos^2(x/2)
sin(x/2)/cos(x/2)
tan(x/2)
dtan(x/2)/dx = 1/2 (sec^2(x/2)) and were done!

[schaa]

I NEVER SAID I THOUGHT I COULD TAKE THE DERIVATIVE

[AlgyCuber]

for #3, i use the identity and i get tan(x/2), diff that and i get 1/2 sec^2(x/2)

[emanuellupascu]

I’m always excited when you post on YT!!😆

[MrRyanroberson]

alright.
1, easy enough, same steps and solution
2: push the x into the radical to ignore the product rule and get (18*2x - 4x^3)/2sqrt(18x^2-x^4) = 2(9-x^2)/sqrt(18-x^2) which also equals 2(3-x)(3+x)/sqrt(18-x^2)
3: push the sine down-down to get (sin^-1 (1 + cos))^-1 and by the chain rule get -(-cos(1+cos)/sin^2 -1)*sin^2/(1+cos)^2
(cos(1+cos)+sin^2)/(1+cos)^2 = (cos+1)/(1+cos)^2 = 1/(1+cos)

[Apollorion]

Concerning #2: isn't the square of a squareroot of a value x equal to the absolute value of x, instead of just x?

[Generalth]

Was there a fly in the background at 2:30 to 2:40?

[blacklodgeinitiative]

can we buy any of the t-shirts you wear?

[isaacaguilar]

I am new to calculus and I was only able to get 1 and 3 but I overthought 2. I am skipping calculus 1 and going to calculus 2 so I have to learn basic Calc during the summer. Any tips?

[msolec]

#2 can't you put the x inside the radical? it becomes sqrt(18x^2 - x^4) and then you take dx. You get (36x - 4x^3) / 2sqrt(18x^2 - x^4)

[Kino-Imsureq]

number 1 is so easy xDDD was able to solve it before you did lol

[Sid-ixqr]

5:12 People got triggered because the denominator wasn't rationalised.

[ahmsaj]

Could you please solve this equation integrate(1 - n ) cos (1+1/2pi)n dn

[alwysrite]

why r u wearing a wall clock on your wrist ? : )

[patrickgleason]

1.) cosx 2.) something with x in it 3.) I don’t know the derivative of tan(x/2)

[amitlevy]

hey bprp, love the vids, I'm a highschool student interested in math and got into an argument with a friend of mine about whether or not 0.999... = 1. Can you please make a video explaining the answer and why?

[simpletn]

Wait aren't these basic differentiation?

[mattgsm]

#YAY! What's the inverse function of f(x)=(2^(x-1)) * ((2^x) - 1)