Find dy/dx 7x+5y^2=1

Problem

7*x+5*y2=1

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x

d()/d(x)*(7*x+5*y2)=d(1)/d(x)

2. Apply the sum rule and differentiate the first term.

(d(7)*x)/d(x)+(d(5)*y2)/d(x)=0

3. Apply the chain rule to the term involving y

7+10*yd(y)/d(x)=0

4. Isolate the term containing d(y)/d(x) by subtracting 7 from both sides.

10*yd(y)/d(x)=−7

5. Solve for d(y)/d(x) by dividing both sides by 10*y

d(y)/d(x)=−7/(10*y)

Final Answer

d(y)/d(x)=−7/(10*y)

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