When y is defined as a function of x

[rab-c]

Homework Statement

find \frac{dy}{dx} when y is defined as a function of x by the equation
y+e^y = x^2

Homework Equations

The Attempt at a Solution

hi all,
do i use implicit differentiation for this? I am not really sure how to start...

 

[Ray Vickson]

Homework Statement

find \frac{dy}{dx} when y is defined as a function of x by the equation
y+e^y = x^2

Homework Equations

The Attempt at a Solution

hi all,
do i use implicit differentiation for this? I am not really sure how to start...

Should you use implicit differentiation? Well, why don't you try it, to see what happens?

RGV

 

[HallsofIvy]

Differentiate both sides of the equation with respect to x. Since the y on the left side is an unknown function of x, yes, you will need to use implicit differentiation.

(But, as Ray Vickson implies, even if you were not sure, you should have tried. Much of mathematics is "try and see if it works".)

 

[rab-c]

y'+e^y y' = 2x
y'(1+e^y) = 2x
y' = \frac{2x}{1+e^y}
I think this is the right answer?