How do you find dy/dx by implicit differentiation of -x^3+xy+y^4=10?

1 Answer
Sahar Mulla ❤
Mar 24, 2018

#-x^3+xy+y^4=10#

Differentiating both the sides,
and applying, product rule to #xy#, #color(red)((d(ab))/dx = (da)/dxb+(db)/dxa# and exponent rule to #x^3# and #y^4#, #color(magenta)((d(x^n))/dx = nx^(n-1)#

#-3x^2+[xy'+x'y]+4y^3y'=0#

#-3x^2+xdy/dx+y+4y^3dy/dx=0#

#(x+4y^3)dy/dx=3x^2-y#

#dy/dx=(3x^2-y)/(x+4y^3)#

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