this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from

Reply 6

B_9710

Original post by Alen.m

this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from

Actually

\displaystyle \frac{d}{dx} y^2 = 2y \frac{dy}{dx}

Reply 7

constellarknight

Use the chain rule. y is defined in terms of x - it isn't just a constant. Thus you have to multiply through by dy/dx.

Original post by Alen.m

this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from

Reply 8

lukejoshjames

Original post by Alen.m

this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from

Have you covered the chain rule yet?

Reply 9

constellarknight

Original post by B_9710

Actually

\displaystyle \frac{d}{dx} y^2 = 2y \frac{dy}{dx}

The original question was x*d/dx(y^2). Multiplying by the x gives 2xy*dy/dx, as required.

Reply 10

username1692103

Original post by Alen.m

this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from

Because if you are being asked to differnetiate y^2 with respect to x (which is what d/dx is asking) you simply cannot do this as you cannot differentiate a function in respect to another function like that. So you have to implicity differnetiate where you use the forumla stated above.

To give you y^2' *dy/dx *x=

2xy dy/dx

If it was asking to differentiate x^2 with respect to x you can do this and is a common result of 2x, hopefully that makes sense?

(edited 8 years ago)

Reply 11

B_9710

Original post by constellarknight

The original question was x*d/dx(y^2). Multiplying by the x gives 2xy*dy/dx, as required.

I know, I was replying to a question that the OP asked after the original post.

Reply 12

Alen.m

Original post by Calzs34

Because if you are being asked to differnetiate y^2 with respect to x (which is what d/dx is asking) you simply cannot do this as you cannot differntiate a function in respect to another function like that. So you have to implicity differntiate where you use the forumla stated above.

To give you y^2' *dy/dx *x

If it was asking to differntiate x^2 with respect to x you can do this and is a common result of 2x, hopefully that makes sense?

used the chain rule to solve it but still not getting it here's how i done it

(edited 8 years ago)

12810431_1988582394699421_47391955_o.jpg114.8KB

Reply 13

Alen.m

Original post by constellarknight

Use the chain rule. y is defined in terms of x - it isn't just a constant. Thus you have to multiply through by dy/dx.

am i missing something here?

12810431_1988582394699421_47391955_o.jpg114.8KB

Reply 14

Alen.m

Original post by lukejoshjames

Have you covered the chain rule yet?

yes i did but i still get the answer as 2xy d/dx

12810431_1988582394699421_47391955_o.jpg114.8KB

Reply 15

username1692103

Original post by Alen.m

used the chain rule to solve it but still not getting it here's how i done it

Original post by Alen.m

am i missing something here?

Try watching this video, you've made a mistake in the way you've differntiated, hopefully this clears it up:

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/implicit_differentiation/v/implicit-differentiation-1

If you're still confused reply back, but it's better to work it out yourself imo :smile: