Question

How do you determine dy/dx given `e^cosy=x^3siny`?

Answer 1

The answer `[dy/dx]=[siny*3x^2]/[e^cosy*siny+x^3*cosy]`

Explanation:

`e^cosy=x^3*siny`

`-e^cosy*siny*(dy/dx)=x^3*cosy*(dy/dx)+siny*3x^2`

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

`[dy/dx][e^cosy*siny+x^3*cosy]=siny*3x^2`

`[dy/dx]=[siny*3x^2]/[e^cosy*siny+x^3*cosy]`