Find dy/dx 11x+3y=7

Problem

11*x+3*y=7

Solution

1. Differentiate both sides of the equation with respect to x

d()/d(x)*(11*x+3*y)=d()/d(x)*7

2. Apply the sum rule and the constant rule for differentiation.

(d(11)*x)/d(x)+(d(3)*y)/d(x)=0

3. Use the chain rule for the term involving y treating y as a function of x

11+3d(y)/d(x)=0

4. Isolate the term containing d(y)/d(x) by subtracting 11 from both sides.

3d(y)/d(x)=−11

5. Solve for d(y)/d(x) by dividing both sides by 3

d(y)/d(x)=−11/3

Final Answer

d(y)/d(x)=−11/3

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