- #1

- 560

- 250

- Homework Statement
- Calculate ##dy/dx## if ##y^2=x##

- Relevant Equations
- Chain Rule

Hi, PF

##y^2=x## is not a function, but it is possible to obtain the slope at any point ##(x,y)## of the equation without previously clearing ##y^2##. It's enough to differentiate respect to ##x## the two members, treat ##y## like a ##x## differentiable function and make use of the Chain Rule to differentiate ##y^2##:

##\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(x)##

##2y\dfrac{dy}{dx}=1##

##\dfrac{dy}{dx}=\dfrac{1}{2y}##

I can't view ##y^2## like a composite function, instead of just a quadratic expression.

Greetings!

##y^2=x## is not a function, but it is possible to obtain the slope at any point ##(x,y)## of the equation without previously clearing ##y^2##. It's enough to differentiate respect to ##x## the two members, treat ##y## like a ##x## differentiable function and make use of the Chain Rule to differentiate ##y^2##:

##\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(x)##

##2y\dfrac{dy}{dx}=1##

##\dfrac{dy}{dx}=\dfrac{1}{2y}##

I can't view ##y^2## like a composite function, instead of just a quadratic expression.

Greetings!