Find the rate of change of q with respect to p when p= (20)/(q^2+5)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to differentiate both sides with respect to p to find the rate of change of q with respect to p,hence, you should use the quotient rule to the left side, such that:

`1 = ((20)'*(q^2 + 5) - 20*(2q*(dq)/(dp)))/((q^2 + 5)^2)`

Since differentiating the constant 20 yields 0, you need to substitute 0 for `(20)'*(q^2 + 5)`  such that:

`((q^2 + 5)^2) = -40q(dq)/(dp)`

`(dq)/(dp) = ((q^2 + 5)^2)/(-40q)`

Hence, evaluating the rate of change of q with respect to p yields `(dq)/(dp) = ((q^2 + 5)^2)/(-40q).`

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