What is the d/(dn)(ln(n^5+5n)) ?

The d/(dn)(ln(n^5+5n)) is (5n^4+5)/(n^5+5n)

What is the first d/(dn)(ln(n^5+5n)) ?

The first d/(dn)(ln(n^5+5n)) is (5n^4+5)/(n^5+5n)

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\frac{d}{d n} (ln (n^{5} + 5 n))

\frac{5 n ^{4} + 5}{n ^{5} + 5 n}

Solution steps

\frac{d}{d n} (ln (n^{5} + 5 n))

Apply the chain rule:

\frac{1}{n ^{5} + 5 n} \frac{d}{d n} (n^{5} + 5 n)

= \frac{1}{n ^{5} + 5 n} \frac{d}{d n} (n^{5} + 5 n)

\frac{d}{d n} (n^{5} + 5 n) = 5 n^{4} + 5

= \frac{1}{n ^{5} + 5 n} (5 n^{4} + 5)

Simplify

\frac{1}{n ^{5} + 5 n} (5 n^{4} + 5) : \frac{5 n ^{4} + 5}{n ^{5} + 5 n}

= \frac{5 n ^{4} + 5}{n ^{5} + 5 n}

\int_{0}^{3} \frac{3}{x ( x - 3 )} d x

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\int \frac{1 - ln ( x )}{x} d x

\int (t^{4} + 5 t^{3} + 4) d t

\frac{\partial}{\partial x} (sin (- 2 x) cos (2 y))

What is the d/(dn)(ln(n^5+5n)) ?
The d/(dn)(ln(n^5+5n)) is (5n^4+5)/(n^5+5n)
What is the first d/(dn)(ln(n^5+5n)) ?
The first d/(dn)(ln(n^5+5n)) is (5n^4+5)/(n^5+5n)