Find dy/dx y^3=x^5

Problem

y3=x5

Solution

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

d(y3)/d(x)=d(x5)/d(x)

2. Apply the power rule and the chain rule to the left side, and the power rule to the right side.

3*y2d(y)/d(x)=5*x4

3. Isolate the derivative by dividing both sides of the equation by 3*y2

d(y)/d(x)=(5*x4)/(3*y2)

Final Answer

d(y)/d(x)=(5*x4)/(3*y2)

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