Question

Find the derivative using the derivative rules?

Answer 1

`(dy)/(dx)=-(3x+2y)/(2x+y)`

Explanation:

we need to differentiate implicitly, and using the product rule on the second term

so differentiating wehave

`d/(dx)(3x^2)+d/(dx)(4xy)+d/(dx)(y^2)=d/(dx)(5)`

`=>6x+4y+4x(dy)/(dx)+2y(dy)/(dx)=0`

rearrange for `(dy)/(dx)`

`4x(dy)/(dx)+2y(dy)/(dx)=-(6x+4y)`

`(dy)/(dx)[4x+2y]=-(6x+4y)`

`(dy)/(dx)=-(6x+4y)/[4x+2y]=-(cancel(2)(3x+2y))/(cancel(2)(2x+y))`

`(dy)/(dx)=-(3x+2y)/(2x+y)`