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Differentiation

Hey guys, I'm trying to differentiate x=y²-y to find the gradient when x=0

so dx/dy=2y-1 do I leave it and solve 0=2y-1 or do I change it to dy/dx=0.5x-1 and substitute in 0? :confused:

Reply 1

BabyMaths

Original post by Rbutton

Hey guys, I'm trying to differentiate x=y²-y to find the gradient when x=0

so dx/dy=2y-1 do I leave it and solve 0=2y-1 or do I change it to dy/dx=0.5x-1 and substitute in 0? :confused:

Find y when x=0. There are two values to find. Substitute these into your dx/dy. Find the reciprocal.

Reply 2

moment of truth

Change it to dy/dx

Or you could do it the way BabyMaths showed. Either way should work.

(edited 9 years ago)

Reply 3

Rbutton

Original post by BabyMaths

Find y when x=0. There are two values to find. Substitute these into your dx/dy. Find the reciprocal.

How can there be two values? There can only be one gradient at any one point?

Reply 4

Rbutton

Original post by moment of truth

Change it to dy/dx

Or you could do it the way BabyMaths showed. Either way should work.

If I switch to dy/dx then I get (1/2x)-1 and which means that 0 can't be substituted in, have I changed it wrong?

Reply 5

BabyMaths

Original post by Rbutton

How can there be two values? There can only be one gradient at any one point?

Certainly there can be two values. If

x=y^2-y

then when x=0 you are solving

y^2-y=0

Reply 6

Rbutton

Original post by BabyMaths

Certainly there can be two values. If

x=y^2-y

then when x=0 you are solving

y^2-y=0

Yes, but it's the gradient so you'll get the same value it'll just be +/- ?

Reply 7

BabyMaths

Original post by Rbutton

Yes, but it's the gradient so you'll get the same value it'll just be +/- ?

I recommend doing a sketch of the graph of

x=y^2-y

so that you understand exactly what you're dealing with. You could also use https://www.desmos.com/calculator

Reply 8

TenOfThem

Original post by Rbutton

Hey guys, I'm trying to differentiate x=y²-y to find the gradient when x=0

so dx/dy=2y-1 do I leave it and solve 0=2y-1 or do I change it to dy/dx=0.5x-1 and substitute in 0? :confused: