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Popular >

d/(dn)((log_{10}(n))^3)

Solution

\frac{d}{d n} ((lo g_{10} (n))^{3})

Solution

\frac{3 lo g _{10} ( n ) ^{2}}{ln ( 10 ) n}

Solution steps

\frac{d}{d n} ((lo g_{10} (n))^{3})

Apply the chain rule:

3 (lo g_{10} (n))^{2} \frac{d}{d n} (lo g_{10} (n))

= 3 (lo g_{10} (n))^{2} \frac{d}{d n} (lo g_{10} (n))

\frac{d}{d n} (lo g_{10} (n)) = \frac{1}{n ln ( 10 )}

= 3 (lo g_{10} (n))^{2} \frac{1}{n ln ( 10 )}

Simplify

3 lo g_{10} (n)^{2} \frac{1}{n ln ( 10 )} : \frac{3 lo g _{10} ( n ) ^{2}}{ln ( 10 ) n}

= \frac{3 lo g _{10} ( n ) ^{2}}{ln ( 10 ) n}

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Frequently Asked Questions (FAQ)

What is the d/(dn)((log_{10}(n))^3) ?
The d/(dn)((log_{10}(n))^3) is (3log_{10}(n)^2)/(ln(10)n)
What is the first d/(dn)((log_{10}(n))^3) ?
The first d/(dn)((log_{10}(n))^3) is (3log_{10}(n)^2)/(ln(10)n)