For the equation given below, evaluate dy/dx at the point (1, ½). y/(x-3y)= x^5-2 dy/dx at the point (1, ½)=

For the equation given below, evaluate dy/dx at the point (1, ½). y/(x-3y)= x^5-2
dy/dx at the point (1, ½)=

y/(x-3y)= x^5-2
y = (x-3y)(x^5-2)
y = x^6 -2x -3x^5y +6y

differentiate both sides with respect to x
dy/dx = 6x^5 - 2 - 3 (5x^4) y -3x^5 dy/dx + 6 dy/dx

dy/dx [ 1+3x^5-6] = 6x^5-15x^4y
dy/dx = (6x^5-15x^4y) / (3x^5-5)

substitute x=1; y=1/2
dy/dx = (6-15/2) / (3-5) = 3/4