Find dy/dx 2 square root of x+ square root of y=3

Problem

2√(,x)+√(,y)=3

Solution

1. Rewrite the equation using rational exponents to make differentiation easier.

2*x(1/2)+y(1/2)=3

2. Differentiate both sides of the equation with respect to x applying the chain rule to the term involving y

d()/d(x)*(2*x(1/2)+y(1/2))=d(3)/d(x)

3. Apply the power rule to each term on the left side.

2⋅1/2*x(−1/2)+1/2*y(−1/2)d(y)/d(x)=0

4. Simplify the coefficients and rewrite the negative exponents as square roots in the denominator.

1/√(,x)+1/(2√(,y))d(y)/d(x)=0

5. Isolate the term containing d(y)/d(x) by subtracting 1/√(,x) from both sides.

1/(2√(,y))d(y)/d(x)=−1/√(,x)

6. Solve for d(y)/d(x) by multiplying both sides by 2√(,y)

d(y)/d(x)=−(2√(,y))/√(,x)

Final Answer

d(y)/d(x)=−(2√(,y))/√(,x)

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