Use your explicit equation for y in terms of x to estimate

Question

a. Using implicit differentiation of the equation

sin(x² + y) = x² - 2x

to find dy/dx.

b. Unfortunately, the astronomers tell Brutus that all of the Ohio supercomputers are scheduled for use for the next three months. This makes Brutus sad. (Brutus wants to use the supercomputers to estimate a point on the curve of this new sketch.) Undeterred, Brutus figures out a why around this problem:

Solve for y in the equation

i. sin(x² + y) = x² - 2x.

ii. Use your explicit equation for y in terms of x to find dy/dx.

iii. Use your explicit equation for y in terms of x to estimate a point on the graph and find the value of dy/dx evaluated at this point.