Question

Find d y/d x by implicit differentiation
4+3 x=sin(x y⁴)

Answer 1

To find dy/dx by implicit differentiation for the given equation 4 + 3x = sin(xy⁴), differentiate both sides of the equation using the chain rule.

Step-by-step explanation:

To find dy/dx by implicit differentiation for the given equation 4 + 3x = sin(xy⁴), we need to differentiate both sides of the equation with respect to x using the chain rule. Let's proceed step-by-step:

1. Differentiate the left side with respect to x: d(4 + 3x)/dx = 0 + 3 = 3
2. For the right side, we have an implicit function sin(xy⁴), so we need to differentiate it using the chain rule:
3. Let u = xy⁴.
4. Then, dy/dx = (dy/du) * (du/dx).
5. After finding dy/du and du/dx, multiply them together.