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c3 maths differentiation question!!!!!!

given that

x = sec^2 y + tan y

show that

dy/dx = cos^2 y / 2tan y + 1

thank you, who ever does this, i really appreciate your help
its a hard question, so could you set it out in easy steps. thanks again!

I think you mean

dy/dx = cos^2y / ( 2tany + 1)

If you weren't looking at it like this then you should now be able to do it fairly easily.

OP

no i kno wat i wrote.
it was correct
if u cant help, then its kool
but can some one help me with the original equation

ash213

given that

x = sec^2 y + tan y

show that

dy/dx = cos^2 y / 2tan y + 1

thank you, who ever does this, i really appreciate your help
its a hard question, so could you set it out in easy steps. thanks again!

differentiate sec²y by chain rule
x=sec²y let sec y = t so that dt/dy = secy.tany
x= t² so dx/dt = 2t
dx/dy = dx/dt x dt/dy = 2t.secy.tany = 2 sec²y.tany

include +tany
dx/dy = 2 sec²y.tany + sec²y = sec²y(2tany+1) = (2tany+1) /cos²y
Invert.

Aitch

OP

no i kno wat i wrote.
it was correct
if u cant help, then its kool
but can some one help me with the original equation

ash213

no i kno wat i wrote.
it was correct
if u cant help, then its kool
but can some one help me with the original equation

See solution above!

Isnt dx/dy cos^2 y / (2tan y + 1) and not dy/dx...?

Vazzyb

Isnt dx/dy cos^2 y / (2tan y + 1) and not dy/dx...?

The last line of my working has to be inverted to get q.e.d.

Aitch

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