derivatives and implicit differentiation: xy^2-6x^3+4y^4=10

[crzymath]

i did this problem which asked me to find the first derivative but i got it wrong, anyone spot my mistake?

xy[sup:1g9a4zu3]2[/sup:1g9a4zu3]-6x[sup:1g9a4zu3]3[/sup:1g9a4zu3]+4y[sup:1g9a4zu3]4[/sup:1g9a4zu3]=10
=[1]2yy[sup:1g9a4zu3]1[/sup:1g9a4zu3]-18x[sup:1g9a4zu3]2[/sup:1g9a4zu3]+16y[sup:1g9a4zu3]3[/sup:1g9a4zu3]=0 <---i took the derivative for everything
=2yy[sup:1g9a4zu3]1[/sup:1g9a4zu3]+16y[sup:1g9a4zu3]3[/sup:1g9a4zu3]=18x[sup:1g9a4zu3]2[/sup:1g9a4zu3]
y[sup:1g9a4zu3]1[/sup:1g9a4zu3](2y+16y[sup:1g9a4zu3]2[/sup:1g9a4zu3])=18x[sup:1g9a4zu3]2[/sup:1g9a4zu3]
y[sup:1g9a4zu3]1[/sup:1g9a4zu3]=18x[sup:1g9a4zu3]2[/sup:1g9a4zu3]/(2y+16y[sup:1g9a4zu3]2[/sup:1g9a4zu3])

i dont know what i did wrong, but for some reason on my test i got all the questions that asked to do the first deriv, wrong-what am i doin incorrect?

also, this problem asks me to do implicit differentiation to solve the problem.

x[sup:1g9a4zu3]2[/sup:1g9a4zu3]+3xy+y[sup:1g9a4zu3]3[/sup:1g9a4zu3]=10

im point blank on this one. basically im studyin for my final exam and this is all of the stuff we learned months ago-so i can barely remember any of the material.
can anyone give me pointers on how to derivative problems properly.

much appreciated!!

 

[wjm11]

Re: derivatives and implicit differentiation

For the derivative of xy^2 you must use the chain rule, power rule, and the product rule:

x(2y)(dy/dx) + y^2

Derivative of 4y^4 with respect to x is

(16y^3)(dy/dx)

(with compliments to Subhotosh for picking up my typo/error)

 

[galactus]

Re: derivatives and implicit differentiation

\(\displaystyle x^{2}+3xy+y^{3}=10\)

I will step through this one as a refresher. OK?.

When you differentiate wrt y, tack on a y'. When you have an xy, use the product rule.

\(\displaystyle 2x+\underbrace{3xy'+3y}_{\text{product rule for 3xy}}+3y^{2}y'=0\)

\(\displaystyle 3xy'+3y^{2}y'=-2x-3y\)

\(\displaystyle y'(3x+3y^{2})=-2x-3y\)

\(\displaystyle y'=\frac{-(2x+3y)}{3(x+y^{2})}\)

Remember now?.

 

[crzymath]

ok-i redid the problem and this is what i got:

problem:
xy[sup:2p0zqal5]2[/sup:2p0zqal5]-6x[sup:2p0zqal5]3[/sup:2p0zqal5]+4y[sup:2p0zqal5]4[/sup:2p0zqal5]=10

answer:
dx/dy = -y[sup:2p0zqal5]2[/sup:2p0zqal5]+18x[sup:2p0zqal5]2[/sup:2p0zqal5]/2xy+16y[sup:2p0zqal5]3[/sup:2p0zqal5]

this right? i dont have an answer in the back of the book so it wud help me if you let me know!

thanks!

 

[crzymath]

Re: derivatives and implicit differentiation

\(\displaystyle x^{2}+3xy+y^{3}=10\)

I will step through this one as a refresher. OK?.

When you differentiate wrt y, tack on a y'. When you have an xy, use the product rule.

\(\displaystyle 2x+\underbrace{3xy'+3y}_{\text{product rule for 3xy}}+3y^{2}y'=0\)

\(\displaystyle 3xy'+3y^{2}y'=-2x-3y\)

\(\displaystyle y'(3x+3y^{2})=-2x-3y\)

\(\displaystyle y'=\frac{-(2x+3y)}{3(x+y^{2})}\)

Remember now?.

thanks! this REALLY helped me!! i did some sample problems and i got them rite! this was very helpful! thanks alot!

 

[galactus]

ok-i redid the problem and this is what i got:

problem:
xy[sup:1g19qqmx]2[/sup:1g19qqmx]-6x[sup:1g19qqmx]3[/sup:1g19qqmx]+4y[sup:1g19qqmx]4[/sup:1g19qqmx]=10

answer:
dx/dy = -y[sup:1g19qqmx]2[/sup:1g19qqmx]+18x[sup:1g19qqmx]2[/sup:1g19qqmx]/2xy+16y[sup:1g19qqmx]3[/sup:1g19qqmx]

this right? i dont have an answer in the back of the book so it wud help me if you let me know!

thanks!

YES, that is right. See, you can do it.

Except, shouldn't that be dy/dx and not dx/dy?.

 

[crzymath]

sorry my bad-it should be dx/dy...lol

ok-im gonna post another problem that involves sin/cos-do u mind checkin that one for me in a bit?

 

[galactus]

So it is dx/dy. That's unusual. That is a different matter then. I have been doing them the usual dy/dx way.

To do dx/dy we just treat x as we did y.

If we want dx/dy, then it would be \(\displaystyle 2xy+x'y^{2}-18x^{2}x'+16y^{3}=0\)

 

[crzymath]

can anyone help me please? i have two days to study for my final so all help will be appreciated!

 

[mmm4444bot]

... basically im studyin for my final exam and this is all of the stuff we learned months ago-so i can barely remember any of the material.
can anyone give me pointers on how to derivative problems properly.

Don't you take notes?

 

[crzymath]

yes but our class notes are more lecture and less problems/examples. so they really dont help much.
this class is mostly a teach yourself class. teacher doesnt help much.

 

[mmm4444bot]

... but our class notes are more lecture and less problems/examples. so they really dont help ...

Lectures about what, exactly?