The following calculation shows the steps to compute the derivative of P(q) = -2

Question

The following calculation shows the steps to compute the derivative of P(q) = -2q + log(qq(q + 5)q+5). Fill in the boxes so that each expression is mathematically correct and follows from the previous one. The logarithm of a product is the sum of the logarithms of the factors: P(q) = -2q + log(qq) + log((q + 5)q+5) Using the formula log (ab) = log (): P(q) = - + log(q) + (q + 5)) log( + 5) Taking derivatives to both sides of the equation: P?(q) = d / dq (-2 + q + ()log(q +5)) Differentiate the sum term by term and factor out constants: p?(q) = (d / dq q) + (d / d ((q + 5) log(q + 5))) + d / d (q )

Explanation / Answer

Using the formula... = b log (a)

P(q) = -2q + q log (q) + (q+5) log (q + 5)

P'(q) = d/dq (-2q + q log q + (q+5) log (q+5))

Differentiate the sum...

P'(q) = -2 (d/dq q) + (d/dq ((q+5) log(q+5)) + d/dq (q log q)

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