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Popular Calculus >

d/(dn)((n+1)^n)

Solution

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

Solution

(ln (n + 1) + \frac{n}{n + 1}) (n + 1)^{n}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

(n + 1)^{n} = e^{n l n (n + 1)}

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

Apply the chain rule:

e^{n l n (n + 1)} \frac{d}{d n} (n ln (n + 1))

= e^{n l n (n + 1)} \frac{d}{d n} (n ln (n + 1))

\frac{d}{d n} (n ln (n + 1)) = ln (n + 1) + \frac{n}{n + 1}

= e^{n l n (n + 1)} (ln (n + 1) + \frac{n}{n + 1})

e^{n l n (n + 1)} = (n + 1)^{n}

= (ln (n + 1) + \frac{n}{n + 1}) (n + 1)^{n}

Graph

Popular Examples

derivative of f(x)=(sin(5x))/(3x)

d er i v a t i v e f (x) = \frac{sin ( 5 x )}{3 x}

integral of 1/(sqrt(1-49x^2))

\int \frac{1}{1 - 49 x ^{2}} d x

integral of (x^2-25)/(x-5)

\int \frac{x ^{2} - 25}{x - 5} d x

derivative of 7e^x+2/(\sqrt[3]{x})

\frac{d}{d x} (7 e^{x} + \frac{2}{3 x})

integral from 0 to pi of sec^2(x)

\int_{0}^{π} sec^{2} (x) d x

Frequently Asked Questions (FAQ)

What is the d/(dn)((n+1)^n) ?
The d/(dn)((n+1)^n) is (ln(n+1)+n/(n+1))(n+1)^n
What is the first d/(dn)((n+1)^n) ?
The first d/(dn)((n+1)^n) is (ln(n+1)+n/(n+1))(n+1)^n