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new hand
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Homework Statement
3(√x2+xy)-2x2+10=0
The Attempt at a Solution
There are x and y on the same side. If I expand it directly, it is so complicated!
Can anyone show me the full step?
Thanks!
new hand said:Homework Statement
3(√x2+xy)-2x2+10=0The Attempt at a Solution
There are x and y on the same side. If I expand it directly, it is so complicated!
Can anyone show me the full step?
Thanks!
That's really nice! Thank you anyway ^^MidgetDwarf said:Yes, implicit differentiation. Or you can kick -2x^2+10 to the right hand hand and multiply both sides by the power of 1/3. It is the same amount of work. I cannot show you the full steps because it is against site policy. You have to attempt it first.
Are you familiar with implicit differentiation? I won't go into why it works just give you an algorithm.
If not, I will give an example.
yx=3+x
we take the derivative (dy/dx) on both sides of the equation.
so (dy/dx)(yx)=(dy/dx)(3+x)
working with the right side we have,
(dy/dx)3 + (dy/dx)x or we can just keep it the same as the above step.
we end up on the right with 0+1=1.
now working with the left hand side, we have
(dy/dx)(yx). Apply the product rule of differentiation.
y(dy/dx)x+x(dy/dx)y =y + x(dy/dx)
now combine the left and right hand signs.
y+x(dy/dx)=1
Isolate the (dy/dx).
(dy/dx)= (1-y)/x. You can get rid of the y by using the original equation an isolating for y and substituting that y into the final equation.
In short, you preform differentiation through out the whole problem. Every time you see y remember to keep (dy/dx) next to it.
I know this explanation is hand-wavy, but I don't want to go into the specifics.
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