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Popular Calculus >

derivative of nlog_{2}(n)

Solution

derivative of

n lo g_{2} (n)

Solution

lo g_{2} (n) + \frac{1}{ln ( 2 )}

Solution steps

\frac{d}{d n} (n lo g_{2} (n))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = n, g = lo g_{2} (n)

= \frac{d n}{d n} lo g_{2} (n) + \frac{d}{d n} (lo g_{2} (n)) n

\frac{d n}{d n} = 1

\frac{d}{d n} (lo g_{2} (n)) = \frac{1}{n ln ( 2 )}

= 1 \cdot lo g_{2} (n) + \frac{1}{n ln ( 2 )} n

Simplify

1 \cdot lo g_{2} (n) + \frac{1}{n ln ( 2 )} n : lo g_{2} (n) + \frac{1}{ln ( 2 )}

= lo g_{2} (n) + \frac{1}{ln ( 2 )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of nlog_{2}(n) ?
The derivative of nlog_{2}(n) is log_{2}(n)+1/(ln(2))
What is the first derivative of nlog_{2}(n) ?
The first derivative of nlog_{2}(n) is log_{2}(n)+1/(ln(2))