Question

find dy/dx by implicit differentiation x^2+y^2=49

Answer 1

Hey! Welcome to OpenStudy!

So we start with our power rule on each term, yes?

Answer 2

\[\Large\rm \color{royalblue}{(x^2+y^2)'}=\color{royalblue}{(49)'}\]We have to apply the chain rule on the left side,
\[\Large\rm 2x\color{royalblue}{(x)'}+2y\color{royalblue}{(y)'}=0\]We'll apply it to both x and y just to help get this concept across.

Answer 3

The derivative of x with respect to x is simply 1,\[\Large\rm 2x\color{orangered}{(1)}+2y\color{royalblue}{(y)'}=0\]The derivative of y with respect to x, we call that y',\[\Large\rm 2x\color{orangered}{(1)}+2y~\color{orangered}{y'}=0\]

Answer 4

Derivative of the constant side gave us zero.
And then just solve for y'.

Mmm what do you think? Too confusing?
Questions?

Answer 5

thank you so much!! which value would you use to solve for y'