Quick differentiation question (1 Viewer)

[LoveHateSchool]

I'm trying to differentiate V=5.4(2sinθ + sinθcosθ) .
And then deriving that derivative.

Can someone please step me through, I'm brain fried and failing at it and the rest of the Q will be easy after this.

 

[Timske]

Answer is , 10.8cosx + 5.4cos2x
v = 5.4(2sinx+cosxsinx) , expand
v = 10.8sinx + 5.4sinxcosx , we know sinxcosx = 1/2sin2x
v = 10.8sinx + 5.4/2sin2x
differentiate d/dx sinx = cosx and d/dx sin2x=2cos2x

dv/dx = 10.8cosx + 5.4/2*2*cos2x

 

[LoveHateSchool]

Answer is , 10.8cosx + 5.4cos2x
v = 5.4(2sinx+cosxsinx) , expand
v = 10.8sinx + 5.4sinxcosx , we know sinxcosx = 1/2sin2x
v = 10.8sinx + 5.4/2sin2x
differentiate d/dx sinx = cosx and d/dx sin2x=2cos2x

dv/dx = 10.8cosx + 5.4/2*2*cos2x

Thank you so much, just two quick Qs.
1) How do we know sinθcosθ is 1/2sin2x ?
2) For the answer to be 5.4(2cosθ + 2cos^2θ-1), did they just factorize it? I'm still messing it up

 

[Timske]

1) well sin2x= 2sinxcosx therefore 1/2sin2x = 1/2*2sinxcosx = sinxcos
2) The answer is 10.8cosx+5.4cos2x, factorise 5.4 out -> 5.4(2cosx+cos2x) , applying the identity cos2x = 2cos^2x - 1 -> 5.4(2cosx + 2cos^2x-1)

 

[enoilgam]

1) well sin2x= 2sinxcosx therefore 1/2sin2x = 1/2*2sinxcosx = sinxcos
2) The answer is 10.8cosx+5.4cos2x, factorise 5.4 out -> 5.4(2cosx+cos2x) , applying the identity cos2x = 2cos^2x - 1 -> 5.4(2cosx + 2cos^2x-1)

Its been a while since I have done this, but isnt that a 3 unit thing?

 

[Shadowdude]

Its been a while since I have done this, but isnt that a 3 unit thing?

Yeah it is.

 

[Amundies]

Yeah, those are 3U trig identities.

 

[Timske]

Thank you so much, just two quick Qs.
1) How do we know sinθcosθ is 1/2sin2x ?
2) For the answer to be 5.4(2cosθ + 2cos^2θ-1), did they just factorize it? I'm still messing it up

Get that without 3u identities

 

[nightweaver066]

I must be half asleep. Already much discussion in this thread..

 

[LoveHateSchool]

Thank you so much for all the discussion guys, and nightweaver you worked solution is fantastic, I can step my way through it and see where I was screwing up now <3

 

[Come at me]

Use product rule to diff sin . cos (u cant use 3u identities in 2u)