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)