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how would you differentiate

16x+4y-19=0?
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p29
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12
?????
16x+4y-19=0
differentiated is 16+4dy/dx+0

dy/dx=-16/4
Dy/dx=-4
If you've been asked to differentiate with respect to xx, first rearrange so to that you get an equation starting with y=y=.

Then, differentiate as normal.
Original post by p29
16x+4y-19=0?


Like the above said

rearrange for y

4y=19-16x
y=19/4 -4x

then differentiate and you've got an answer
You have two options.

Differentiating dy by dx means with respect to x, in terms of y. However your equation has a term with respect to y inside.

So the 'simple' solution is to re-arange for y.
16x+4y-19=0
y = 1/4(19-16x)

dy/dx = -4

now you have an equation in terms of y with respect to x. Which you can differentiate dy by dx.

Otherwise (depending on if you've learned), you can differentiate implicitly, this isn't so much of an issue for your equation as it can be re-arrange fairly simply. However for equations that are a lot more complex, implicitly is the way to go.

d [16x+4y-19] by dx
16 + 4 dy/dx = 0
4 dy/dz = -16
dy/dx = -4

so you now have the differential of -4

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