Calculus Help

Question

Determine the slope of the tangent line at (0,0) if 32e^x+10e^y=80x−2y.



m =

Answer 1

32e^x + 10e^y = 80x -2y This cannot be solved for y(x) and dy/dx taken, so differentiate implicitly:

32e^x + 10e^y dy/dx = 80 - 2 dy/dx

solve for dy/dx by rearranging

dy/dx = (80 - 32e^x)/(2+10e^y)

Now substitute in (0,0) and find slope.