Find dy/dx x^4+y^4=16

Problem

x4+y4=16

Solution

1. Differentiate both sides with respect to x using the power rule and the chain rule for the term involving y

d(x4)/d(x)+d(y4)/d(x)=d(16)/d(x)

2. Apply the chain rule to the y4 term, treating y as a function of x

4*x3+4*y3d(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 4*x3 from both sides.

4*y3d(y)/d(x)=−4*x3

4. Solve for dy/dx by dividing both sides by 4*y3

d(y)/d(x)=(−4*x3)/(4*y3)

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

d(y)/d(x)=−(x3)/(y3)

Final Answer

d(y)/d(x)=−(x3)/(y3)

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