Answer :
Final answer:
To find y' by implicit differentiation, differentiate both sides of the equation and solve for y' by isolating the term.
Explanation:
To find y' by implicit differentiation, we differentiate both sides of the equation with respect to x. Taking the derivative of 9x^7 y^5 with respect to x gives us 63x^6 y^5 + 45x^7y^4y', and the derivative of 4x with respect to x is simply 4. Setting these derivatives equal to each other, we have 63x^6 y^5 + 45x^7y^4y' = 4. From here, we can rearrange the equation and solve for y' by isolating the term: 45x^7y^4y' = 4 - 63x^6 y^5 y' = (4 - 63x^6 y^5) / (45x^7y^4).
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