Question

How do you implicitly differentiate `y / [ x - 7y ] = x^4 + 9`?

Answer 1

`(dy)/(dx)=(5x^4-28x^3y+9)/(7x^4+64)`

Explanation:

`y/(x-7y)=x^4+9` `hArry=(x^4+9)(x-7y)`

Hence `(dy)/(dx)=(x^4+9)(1-7(dy)/(dx))+4x^3(x-7y)`

or `(dy)/(dx)=x^4+9-7(dy)/(dx)(x^4+9)+4x^4-28x^3y`

or `(dy)/(dx)+7(dy)/(dx)(x^4+9)=5x^4-28x^3y+9`

or `(dy)/(dx)=(5x^4-28x^3y+9)/(1+7(x^4+9))`

or `(dy)/(dx)=(5x^4-28x^3y+9)/(7x^4+64)`