# 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: