Question

Question #37cdd

Answer 1

`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)`

Answer 2

`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)`