[LimeTree.]

x=tan(3y+1)


What would be dx/dy?

Cheers

[roar558]

(Original post by LimeTree.)
x=tan(3y+1)


What would be dx/dy?

Cheers

3sec^2(3y+1)
using differentiation by substitution

[Spungo]

d(tan x)/dx = (sec x)^2

Try using the substitution u = 3y+1

[LimeTree.]

Thankyou!

How do I use the substitution?

Sorry, I just really dont understand this

[roar558]

(Original post by LimeTree.)
Thankyou!

How do I use the substitution?

Sorry, I just really dont understand this

if x=tanu
dx/du=sec^2u
dx/dy=dx/du x du/dx
u=ax
du/dx=a
dx/dy=asec^2 ax

[LimeTree.]

(Original post by roar558)
if x=tanu
dx/du=sec^2u
dx/dy=dx/du x du/dx
u=ax
du/dx=a
dx/dy=asec^2 ax

Thankyou very much!

So x=tan(4y+2)
x=tanu
dx/du=sec^2u

u=4y+2
du/dx=4

dx/dy *du/dx = 4Sec^2(4y+2)



So use chain rule with substitution?

Thanks

[Zagreus_92]

Another way to think about it is to use the identity that and then to use quotient rule so in your case:







So that's always an option if you don't want to use substitution

[roar558]

(Original post by LimeTree.)
Thankyou very much!

So x=tan(4y+2)
x=tanu
dx/du=sec^2u

u=4y+2
du/dx=4

dx/dy *du/dx = 4Sec^2(4y+2)



So use chain rule with substitution?

Thanks

Yep essentially, np