Find dy/dx (y-3)^2=4(x-5)

Problem

(y−3)2=4*(x−5)

Solution

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

d(y−3)/d(x)=d(4*x−20)/d(x)

2. Apply the power rule and the chain rule to the left side, and differentiate the linear expression on the right side.

2*(y−3)d(y)/d(x)=4

3. Isolate the derivative by dividing both sides of the equation by 2*(y−3)

d(y)/d(x)=4/(2*(y−3))

4. Simplify the fraction by dividing the numerator and the denominator by their greatest common factor, which is 2

d(y)/d(x)=2/(y−3)

Final Answer

d(y)/d(x)=2/(y−3)

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