Final answer:
To find dy/dx by implicit differentiation for the equation 7xy = 5x²y², differentiate both sides of the equation with respect to x. Use the product rule and chain rule to differentiate each side separately, then solve for dy/dx.
Step-by-step explanation:
To find dy/dx by implicit differentiation for the equation 7xy = 5x²y², we will differentiate both sides of the equation with respect to x.
Starting with the left side of the equation, we can use the product rule for differentiation: (d/dx)(7xy) = 7y + 7x(dy/dx).
For the right side of the equation, we will use the chain rule: (d/dx)(5x²y²) = 10xy² + 5x²(2ydy/dx).
Setting these two derivatives equal to each other, we get 7y + 7x(dy/dx) = 10xy² + 10x²y(dy/dx). Simplifying and rearranging the equation, we can solve for dy/dx: dy/dx = (10xy² - 7y) / (7x - 10yx²).