Question

What is the derivative of y^3+xe^4=3x^2-10?

Answer 1

`{y}^(3) + x {e}^(4) = 3 {x}^(2) - 10`

introduce dy/dx :

`\frac{d( {y}^(3) + x {e}^(4) ) }{dx} = \frac{d( {3x}^(2) - 10) }{dx} \\ \\ 3 {y}^(2) (dy)/(dx) + {e}^(4) = 6x - 0 \\ \\ {3y}^(2) (dy)/(dx) = 6x - {e}^(4) \\ \\ { \boxed{ \boxed{(dy)/(dx) = \frac{6x - {e}^(4) }{ {3y}^(2) } }}}`