Find dy/dx 5y^2=(4x-3)/(4x+3)

Problem

5*y2=(4*x−3)/(4*x+3)

Solution

1. Differentiate implicitly with respect to x on the left side of the equation using the power rule and chain rule.

(d(5)*y2)/d(x)=10*yd(y)/d(x)

2. Apply the quotient rule to the right side of the equation, where the rule is d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

d()/d(x)(4*x−3)/(4*x+3)=((4*x+3)*(4)−(4*x−3)*(4))/((4*x+3)2)

3. Simplify the numerator of the derivative on the right side.

(16*x+12−(16*x−12))/((4*x+3)2)=24/((4*x+3)2)

4. Equate the results from the left and right sides to form a new equation.

10*yd(y)/d(x)=24/((4*x+3)2)

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

d(y)/d(x)=24/(10*y*(4*x+3)2)

6. Reduce the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2

d(y)/d(x)=12/(5*y*(4*x+3)2)

Final Answer

d(y)/d(x)=12/(5*y*(4*x+3)2)

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