Find dy/dx square root of x+ square root of y=4

Problem

√(,x)+√(,y)=4

Solution

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

√(,x)+√(,y)=4

x(1/2)+y(1/2)=4

2. Differentiate both sides of the equation with respect to x applying the Power Rule and the Chain Rule for the term involving y

d()/d(x)*(x(1/2)+y(1/2))=d()/d(x)*4

1/2*x(−1/2)+1/2*y(−1/2)d(y)/d(x)=0

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

1/(2√(,y))d(y)/d(x)=−1/(2√(,x))

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

d(y)/d(x)=−(2√(,y))/(2√(,x))

d(y)/d(x)=−√(,y)/√(,x)

Final Answer

d(y)/d(x)=−√(,y/x)

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