trig function differentiation question! (1 Viewer)

[!*bella*!]

ok so

the integral of cos ax = 1/a sin ax

therefore, doesn't it follow that

the derivative of sin ax = cos ax

therefore, why is the derivative of sin 3x = 3 cos 3x?

sorri if is a silly question i just dont understand WHY you have to apply the function of a function rule?? answer if u know.

 

[withoutaface]

If we look at sinax

d/dx(sinax)=a(d/dx(1/a sinax)=a(cosax)

Essentially anything you divide by when integrating, you multiply by when differentiating.

 

[Li0n]

You answered yourself? i dont get it.

 

[withoutaface]

You answered yourself? i dont get it.

How did she answer herself?

She was confused as to how something worked, she gave what she thought it was, and then what a textbook said it was, and asked why there was a difference between the two.

 

[!*bella*!]

ok so you know how it has all that stuff on the standard integral sheet?
if you are using that to differentiate something, instead of the 1 on a, it's multiplied by a?

thanks so much btw smarty pants

 

[Xayma]

Yes, you are multiplying by a, to get 1/a equal to 1. If it is originally 1, then you still multiply by a.

 

[paper cup]

I would post, only it would be spamming.
shit, I did it again.
basically you have to anti-differentiate, reverse the process, which means dividing by a.

 

[ngai]

ok so

the integral of cos ax = 1/a sin ax

therefore, doesn't it follow that

the derivative of sin ax = cos ax

therefore, why is the derivative of sin 3x = 3 cos 3x?

sorri if is a silly question i just dont understand WHY you have to apply the function of a function rule?? answer if u know.

lol
lets replace "a" with "3"
ie. "the integral of cos ax = 1/a sin ax" becomes "the integral of cos 3x = 1/3 sin 3x"
carefully note that it becomes "cos3x" and "1/3 sin3x"
now, do u still think the derivative of sin3x is cos3x?...

 

[Li0n]

How did she answer herself?

She was confused as to how something worked, she gave what she thought it was, and then what a textbook said it was, and asked why there was a difference between the two.

ohh
gah i didnt read her actual question , i just derived everything *hits self*