Find dy/dx cos(x)+ square root of y=5

Problem

cos(x)+√(,y)=5

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x and applying the chain rule to the term involving y

d(cos(x))/d(x)+d(√(,y))/d(x)=d(5)/d(x)

2. Apply the derivative rules, where the derivative of cos(x) is −sin(x) and the derivative of y1/2 is 1/2*y(−1/2)d(y)/d(x)

−sin(x)+1/(2√(,y))d(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by adding sin(x) to both sides of the equation.

1/(2√(,y))d(y)/d(x)=sin(x)

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

d(y)/d(x)=2√(,y)*sin(x)

Final Answer

d(y)/d(x)=2√(,y)*sin(x)

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