How do you find #(dy)/(dx)# given #x^3+y+8x=2y^2#?
2 Answers
Jun 1, 2017
Explanation:
Use implicit differentiation and the shorthand
#x^3+y+8x=2y^2#
#d/dx(x^3+y+8x) = d/dx(2y^2)#
#3x^2+y'+8 = 4y*y'#
Now use algebra to solve for
#3x^2+8 = 4y*y'-y'#
#3x^2+8 = y'(4y-1)#
#(3x^2+8)/(4y-1) = y'#
Therefore:
#dy/dx = (3x^2+8)/(4y-1)#
Jun 1, 2017
Explanation:
Write the equation as:
Differentiate both sides with respect to
So that: