Question

Find the slope of the tangent line to the curve
2sin(x)+5cos(y)−4sin(x)cos(y)+x=3π
at the point (3π,5π/2).

Answer 1

2sin(x)+5cos(y)−4sin(x)cos(y)+x=3π

2cos(x) - 5sin(y) dy/dx - 4(cosxcosy + sinx(-siny) dy/dx) + 1 = 0
2cosx - 5siny dy/dx - 4cosxcosy + 4sinxsiny dy/dx + 1 = 0
2(-1) - 5(1)dy/dx - 4(-1)(0) + 4(0)(0)dy/dx + 1 = 0
-2 - 5dy/dx + 1 = 0
-5dy/dx = 1
dy/dx = -1/5

tangent equation:
y - 5π/2 = (-1/5)(x - 3π)

I used

h tt ps://www.desmos.com/calculator

(take out the spaces at the front)
to graph both the original equation and the straight line equation.

I am correct, but what a strange looking graph !!!!