The Student Room Group
Reply 1
cosx isn't it :confused:
Reply 2
yeh cosx
Reply 3
Pretty sure it's not just cosx because I did a question which was to differentiate mod(sin11x) as part of a product and the answer wasn't just 11cos11x.
Reply 4
y = |sinx|
y^2 = sin^2x
2y.dy/dx = 2sinxcosx
dy/dx = sinxcosx/|sinx| = cosx * (sinx/|sinx|)
So it's cosx where sinx is positive and -cosx where sinx is negative.
Reply 5
SilentEar
Pretty sure it's not just cosx because I did a question which was to differentiate mod(sin11x) as part of a product and the answer wasn't just 11cos11x.

I'm pretty sure it should be 11cos11x.
Reply 6
I'm pretty sure it should be 11cos11x.

See my post above, there will be a mod of something in the answer.
Reply 7
Speleo
See my post above, there will be a mod of something in the answer.

mehh im all confused
Reply 8
Ty Speleo
Reply 9
Alternativly by chain rule,

y = |u|, u = sinx

dy/du = sgn(u) = sgn(sinx)

du/dx = cosx

dy/dx = sgn(sinx)cos(x)

BTW the definition of sgn(x) is x/|x|, so the answer is the same as Speleo's.
why is it -cos x when sin x is negative?
Reply 11
dy/dx = cosx * (sinx/|sinx|)
If sinx = -a, where a > 0
dy/dx = cosx * (-a/|-a|)
= cosx * (-a/a)
= -cosx

Oh, I forgot, there are actually three possibilities:
sinx > 0 -> dy/dx = cosx
sinx < 0 -> dy/dx = -cosx
sinx = 0 -> function not differentiable at that point.
Also, not differentiable at multiples of pi, as you would be able to tell from drawing the graph.
Could you please answer Which among the following functions is differentiable on R?(1) |sin x|(2) |cos x|(3) cos|x|(4) sin|x|
Reply 14
Ancient thread. Should probably be moved to maths and closed.

@Doonesbury
Reply 15
Original post by Notnek
Ancient thread. Should probably be moved to maths and closed.

@Doonesbury


Done. I'll leave you to extract the bumping post :wink:
Reply 16
Original post by Doonesbury
Done. I'll leave you to extract the bumping post :wink:

They created a thread so all is well.