Question

How do you find the derivative of `x^2+y^2=e^(3x)`?

Answer 1

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

Explanation:

Here we use the concept of function of a function and whenever we consider derivative w.r.t. `y`, we multiply by `(dy)/(dx)`.

Hence taking derivative of both sides in `x^2+y^2=e^(3x)`

`2x+2y(dy)/(dx)=e^(3x)*3`

or `(dy)/(dx)=(3e^(3x)-2x)/(2y)`