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IScenakon ane Kry Holotmn] PUsH ISee Dealls for mNextiquestion Iou can retry this question below(a) Find the differential dy:y #tan €dy(6) Evaluate dy for the...

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IScenakon ane Kry Holotmn] PUsH ISee Dealls for mNextiquestion Iou can retry this question below(a) Find the differential dy:y #tan €dy(6) Evaluate dy for the given values of € and dz =T/3 and dx 0.05dyQuestion Help: Ovldeo EMessage IDSIrUCtor Submit Question

IScenakon ane Kry Holotmn] PUsH ISee Dealls for m Nextiquestion Iou can retry this question below (a) Find the differential dy: y #tan € dy (6) Evaluate dy for the given values of € and dz =T/3 and dx 0.05 dy Question Help: Ovldeo EMessage IDSIrUCtor Submit Question



Answers

Use Equation 6 to find $ dy/dx $.
$ y \cos x = x^2 + y^2 $

This time they want us to find that relative of the function wise equal to eat. Six x Santa. Let's do you predict role. Take the derivative of the first time really, with 2nd 1 alone. Then leave the first term alone and take the derivative of the second term. And this is ah, derivative six and Iraq's plus goes on your ex.

Equation six says that if we're starting with the equation of the form capital F equals zero that D Y d x will be the negative partial derivative with respect tax over the derivative with respect away. So here we should rewrite this by setting it zero. So let's move everything toe left side and we see that equal zero. So we have this equation that we want and now we should go ahead and find this indicated derivative. So first will just go out and compute this numerator here. So we take the derivative of our new F with respect, Tex. So the first term that will give us e y co sign eggs, then minus one and then minus y oops. Now we go on to the denominator. So, hee, why derivative is just itself. You I still have the constant sine x there. There's no Y in the second term, so that derivative is zero. And in the last term, we have minus X. So therefore, using this equation six Keep my DX away first. Don't forget your negative out here so I'll just go ahead and multiply this by a negative one and the denominator here I'Ll just leave that as it is and there's our answer

We know that after Texas coastline next there for of products is negative. Sign X Therefore of G of x is pi acts this part over here then g prime of X is pi therefore are y prime would be negative pi sign pi x Okay, Part B plug and negative pi sign high over three times negative 0.2 It's in the last 20.1 square root of three times pi.

If you think the equation six, we first have to rewrite our equation in the following form. And then if we do this, then Equation six tells us a formula for the derivative we're trying to find. So let's go ahead and rewrite this so we could obtain F. So notice that if you just subtract, we get zero. So let's just go ahead and call this new equation this new function capital F Sorry about that. I ran out of some room near me back up a capital F. So looking at our equation over here, there's some derivatives we have to find. So let's go find those. So first is the derivative with respect to X so tan in verse and then multiply by the derivative of the inside with respect her ex using the chain rule there. And then we have minus one and also a minus to exploit now for the denominator so very similar for the first one so derivative of Arc Tan square that term in the bottom. And then we'll supply by this term on the inside the derivative of that with respectful why and then here derivative with respect a Y zero and this one negative x clear. So now let's put these together and also noticed the negative sign out here in the very front So we can just go ahead and take this negative sign and just cancel that. Oh, cancel that out. And then we'LL also end up including a negative over here. So we get negative to X y plus one plus two ex wide and let me include that denominator for the first term just for the first time there and then in the denominator. And if anything, you could probably just go ahead and get a common denominator and simplify. But otherwise, here's our final answer.


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