If #y=y^2+5xy# then derivative of y is?

1 Answer
1s2s2p
Jun 13, 2018

#dy/dx=(5y)/(1-2y-5x)#

#dy/dx=-5#

Explanation:

Two ways to do this:
1. #d/dx[y]=d/dx[y^2]+5d/dx[xy]#

#d/dx=dy/dxd/dy#

#dy/dx=dy/dx2y+5y+dy/dx5x#

#dy/dx(1-2y-5x)=5y#

#dy/dx=(5y)/(1-2y-5x)#

  1. Cancel the #y#s:
    #1=y+5x#

#y=1-5x#

#dy/dx=-5#

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