Final answer:
To find dy/dx in the given equation, take the derivative of both sides of the equation with respect to x.
Step-by-step explanation:
To find {{d y}{d x}} in the given equation, we need to take the derivative of the equation with respect to x.
The given equation is y⁹ e⁻²ˣ +2 x⁶-y⁴=4.
Taking the derivative of both sides with respect to x, we get:
9y⁸ e⁻²ˣ (-2) + 12x⁵ - 4y³(dy/dx) = 0
Now, to solve for {{dy/dx}}, divide both sides by 4y³:
{{dy/dx}} = (9y⁸ e⁻²ˣ (-2) + 12x⁵)/(4y³)