The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

C3 Implicit Differentiation Question

Find dy/dx as a fuction of x if y^2 = 2x +1

I don't really understand what to do here. What does it mean 'as a function of x'? Does it mean I can't have y's in my answer? Pls help!
You need to have it in the form dydx=f(x)\frac{dy}{dx} = f(x)
Reply 2
Avatar for B_9710
B_9710
18
Differentiate both sides with respect to x. ddx(y2)=dydx⋅ddy(y2) \frac{d}{dx} (y^2)=\frac{dy}{dx} \cdot \frac{d}{dy} (y^2) .
As for the meaning of a function of x, it means you need it in the form dydx=f(x) \frac{dy}{dx} = f(x) rather than dydx=f(x,y) \frac{dy}{dx} = f(x, y) , basically meaning you don't want any y terms in your expression do dy/dx.
(edited 7 years ago)
Original post by NotNotBatman
You need to have it in the form dydx=f(x)\frac{dy}{dx} = f(x)


So after I differentiate it, I'll need to get rid of the y's?
Original post by B_9710
Differentiate both sides with respect to x. ddx(y2)=dydx⋅ddy(y2) \frac{d}{dx} (y^2)=\frac{dy}{dx} \cdot \frac{d}{dy} (y^2) .
As for the meaning of a function of x, it means you need it in the form dydx=f(x) \frac{dy}{dx} = f(x) rather than dydx=f(x,y) \frac{dy}{dx} = f(x, y) .


Ahh thank you so much!
For the second derivative, will I need to have the answer in the dy/dx = f(x) form before differentiating again?
Original post by IDontKnowReally
So after I differentiate it, I'll need to get rid of the y's?


Yes.

Original post by IDontKnowReally
Ahh thank you so much!
For the second derivative, will I need to have the answer in the dy/dx = f(x) form before differentiating again?


No, but it would be in that form anyway.
Original post by NotNotBatman
Yes.



No, but it would be in that form anyway.


How?
Original post by IDontKnowReally
How?


Just differentiate and rearrange for dydx=f(x)\frac{dy}{dx} =f(x). and use y2=2x+1 y^2= 2x+1 to find y in terms of x.
Original post by NotNotBatman
Just differentiate and rearrange for dydx=f(x)\frac{dy}{dx} =f(x). and use y2=2x+1 y^2= 2x+1 to find y in terms of x.


I understood that but just wasn't sure how it would be in that form before differentiating anyway.
Thanks for all your help!
Reply 9
Avatar for davros
davros
16
Original post by IDontKnowReally
I understood that but just wasn't sure how it would be in that form before differentiating anyway.
Thanks for all your help!


Are you given any restrictions on the domain of y? Because if you're not, you CAN'T write y as a function of x as it stands - there are two possible choices available when you try to take the square root!

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you