Find dy/dx y^4=x^7

Problem

y4=x7

Solution

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

d(y4)/d(x)=d(x7)/d(x)

2. Apply the power rule to both sides, treating y as a function of x on the left side.

4*y3d(y)/d(x)=7*x6

3. Isolate the derivative by dividing both sides of the equation by 4*y3

d(y)/d(x)=(7*x6)/(4*y3)

Final Answer

d(y)/d(x)=(7*x6)/(4*y3)

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