Key to "Compute the derivative of the following function T(n)=nlog2n" - Plainmath

fortdefruitI

Answered question

2021-10-06

Compute the derivative of the following function

T (n) = n \log_{2} n

Answer & Explanation

bahaistag

Skilled2021-10-07Added 100 answers

We use the change of base property of log. Then we use the product rule of the derivative.

T (n) = n \log_{2} n

T (n) = n \frac{\ln (n)}{\ln (2)}

T^{'} (n) = \frac{1}{\ln (2)} \frac{1}{d n} (n \ln (n))

T^{'} (n) = \frac{1}{\ln (2)} [\frac{1}{d n} (n) \ln (n) + n \frac{1}{d n} (\ln (n))]

T^{'} (n) = \frac{1}{\ln (2)} [(1) \ln (n) + n (\frac{1}{n})]

T^{'} (n) = \frac{1}{\ln (2)} [\ln (n) + 1]

Answer:

T^{'} (n) = \frac{1}{\ln (2)} [\ln (n) + 1]

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