Year 12s: what will be the first way you research your future options? >>

Differentiating 3sin^2 x

username3239272

why is dy/dx of 3sin^2 x = 6sin(x)cos(x)
Rather than 3cos^2 x

Reply 1

Notnek

Original post by chanel_666

why is dy/dx of 3sin^2 x = 6sin(x)cos(x)
Rather than 3cos^2 x

It's the chain rule. Do you know how to differentiate something like

4(x^2+3)^5

?

Your one is similar since you can write it as

3(\sin x)^2

If you can't do the non-trig one above then you won't be able to do the trig one.

Reply 2

EmilySarah00

Original post by chanel_666

why is dy/dx of 3sin^2 x = 6sin(x)cos(x)
Rather than 3cos^2 x

Using the chain rule the differential of 3(sinx)^2 is:

The differential of 3u^2 multiplied by the differential of u which in this case = sinx

So that would be 6u * cosx

And since u = sinx that makes it 6sinxcosx

(edited 6 years ago)

Reply 3

username3239272

Original post by Notnek

It's the chain rule. Do you know how to differentiate something like

4(x^2+3)^5

?

Your one is similar since you can write it as

3(\sin x)^2

If you can't do the non-trig one above then you won't be able to do the trig one.

I can do the first one, I didn't think to use the chain rule for the trig one but I see why it works now thanks

Reply 4

_princessxox

why are you doing this at AS it's C3

Reply 5

username3239272

Original post by EmilySarah00

Thanks this makes sense

Original post by _princessxox

why are you doing this at AS it's C3

It's just a bit of cheeky self teach uno

Reply 6

EmilySarah00

Original post by chanel_666

It's just a bit of cheeky self teach uno

You’re welcome :yep:

Also nice one self teaching yourself this if you’re only in AS year, just make sure you prioritise your current subject content! :laugh:

(edited 6 years ago)

Reply 7

username3631354

basically a quick way of doing it is by rewriting it as 3(sinx)^2 which is in the form [f(X)]^n.
It looks scary but stay with me on this as it will save you tons of time in answering these types of questions.
dy/dx would = n[f(x)]^(n-1) x f'(x) so in this example...

1) bring the n down to the front so it's 6 (2x3), 3 was just a constant.

2) write [f(x)] normally but to the power of (n-1) not n, so its 6[sin(x)]^1 or just 6[sin(x)]

3) now take whatever was in the square brackets [f(x)] i.e sin(x) and differentiate this and put it on the end so its 6[sin(x)] multiplied by cos(x) which is just 6sin(x)cos(x).

They key was rewriting sin^2(x) as [sin(x)]^2 remember this is squaring the whole bracket NOT (x)!!

Reply 8

username3239272

Original post by EmilySarah00

You’re welcome :yep:

Also nice one self teaching yourself this if you’re only in AS year, just make sure you prioritise your current subject content! :laugh:

LOL Ive finished my spec for AS I started in summer so Ive been revising
How would I differentiate 2e^x is it still the chain rule cos I didn't think it was needed

(edited 6 years ago)

Reply 9

Notnek

Original post by chanel_666

P

LOL Ive finished my spec for AS I started in summer so Ive been revising
How would I differentiate 2e^x is it still the chain rule cos I didn't think it was needed

The chain rule is used when you have a function within a function so e.g.

e^{x^2}

, this is the function

x^2

inside the function

e^x

2e^x

is more simple : it's just a constant multiplied by a standard function. When there's a constant you leave it alone. Does that help and do you know the answer now?

Reply 10

RDKGames

Study Forum Helper

Original post by chanel_666

P

LOL Ive finished my spec for AS I started in summer so Ive been revising
How would I differentiate 2e^x is it still the chain rule cos I didn't think it was needed

Derivative of

e^x

is an extremely standard thing to know at C3. Look it up and you'll never forget it, then your question becomes extremely trivial.

Reply 11

Notnek

Original post by RDKGames

Derivative of

e^x

is an extremely standard thing to know at C3. Look it up and you'll never forget it, then your question becomes extremely trivial.

It sounds like the OP is doing AS and self-teaching this stuff.

Reply 12

username3239272

Original post by Notnek

The chain rule is used when you have a function within a function so e.g.

e^{x^2}

, this is the function

x^2

inside the function

e^x

2e^x

is more simple : it's just a constant multiplied by a standard function. When there's a constant you leave it alone. Does that help and do you know the answer now?