Question #37cdd

2 Answers
Jul 18, 2017

#dy/dx = - (10 x^4 + 4 x^3 y)/(x^4 + 5 y^4)#

Explanation:

#2 x^5 +x^4 y + y^5 = 36#

differentiate,
#10 x^4 + x^4 dy/dx + y 4 x^3 + 5 y^4 dy/dx = 0#

#x^4 dy/dx + 5 y^4 dy/dx = - (10 x^4 + 4 x^3 y)#

#(x^4 + 5 y^4) dy/dx = - (10 x^4 + 4 x^3 y)#

#dy/dx = - (10 x^4 + 4 x^3 y)/(x^4 + 5 y^4)#

Jul 18, 2017

#dy/dx=-(10x^4+4x^3y)/(x^4+5y^4)#

Explanation:

#"differentiate "color(blue)"implicitly with respect to x"#

#"differentiate "x^4y" using the "color(blue)"product rule"#

#10x^4+(x^4 .dy/dx+4x^3y)+5y^4dy/dx=0#

#rArrdy/dx(x^4+5y^4)=-10x^4-4x^3y#

#rArrdy/dx=-(10x^4+4x^3y)/(4x^4+5y^4)#