Find dy/dx by implicit differentiation given that y satisfies the following equation:
7*x^3-8*x^2*y-2*x*y^2=8, i.e., .
Differentiating we get
d/dx[7*x^3-8*x^2*y-2*x*y^2]=0,
then:
d/dx[7*x^3] - d/dx[8*x^2*y] - d/dx[2*x*y^2]=0,
simplifying the derivative in the first term:
[21*x^2] - d/dx[8*x^2*y] - d/dx[2*x*y^2]=0
Now the second term:
[21*x^2] - [16*x*y+8*x^2 * dy/dx] - d/dx[2*x*y^2]=0
Now the third term:
[21*x^2] - [16*x*y+8*x^2 * dy/dx] - [2*y^2+4*x*y * dy/dx]=0
Now simplify to:
dy/dx = [21*x^2 - 16*x*y - 2*y^2]/[8*x^2 + 4*x*y]
RonL
(please check this carefully)
Checked by PerfectHacker and confiremd.