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Popular >

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}

Popular Examples

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

f (x) = \frac{sin ( 5 x )}{3 x}

derivative of 7/(1-x)derivative of

\frac{7}{1 - x}

derivative of (12/((1-x)^5))

\frac{d}{d x} (\frac{12}{( 1 - x ) ^{5}})

sum from n=3 to infinity of (x^n)/(n!)

n = 3 \sum \infty \frac{x ^{n}}{n !}

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

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