Find dy/da x^4+y^4=a^4

Problem

d(y)/d(a)* for *x^4+y^4=a^4

Solution

1. Identify the variables and the goal. We are finding the derivative of y with respect to a assuming x is a constant and y is a function of a

2. Differentiate both sides of the equation with respect to a Since x is treated as a constant, its derivative is zero.

d(x^4)/d(a)+d(y^4)/d(a)=d(a^4)/d(a)

3. Apply the power rule and the chain rule to the terms. The derivative of x^4 is 0 the derivative of y^4 is 4*y^3d(y)/d(a) and the derivative of a^4 is 4*a^3

0+4*y^3d(y)/d(a)=4*a^3

4. Isolate the derivative term d(y)/d(a) by dividing both sides by 4*y^3

d(y)/d(a)=(4*a^3)/(4*y^3)

5. Simplify the fraction by canceling the common factor of 4

d(y)/d(a)=(a^3)/(y^3)

Final Answer

d(y)/d(a)=(a^3)/(y^3)

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