x=y dy/dx + (dy/dx)^2
You asked:
Given \(x = y\) evaluate the expression \(\frac{d}{dx}\left[y\left( x \right)\right] + {\frac{d}{dx}\left[y\left( x \right)\right]}^{2}\).
MathBot Answer:
\[\frac{d}{dx}\left[y\left( x \right)\right] + {\frac{d}{dx}\left[y\left( x \right)\right]}^{2} = \frac{d}{dy}\left[y\left( y \right)\right] + {\frac{d}{dy}\left[y\left( y \right)\right]}^{2} = \left(\frac{d}{d y} y{\left(y \right)}\right)^{2} + \frac{d}{d y} y{\left(y \right)}\]