What is the d/(dn)(i^{2n+3}) ?

The d/(dn)(i^{2n+3}) is 2ln(i)i^{2n+3}

What is the first d/(dn)(i^{2n+3}) ?

The first d/(dn)(i^{2n+3}) is 2ln(i)i^{2n+3}

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\frac{d}{d n} (i^{2 n + 3})

2 ln (i) i^{2 n + 3}

Solution steps

\frac{d}{d n} (i^{2 n + 3})

Apply exponent rule:

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

i^{2 n + 3} = e^{(2 n + 3) l n (i)}

= \frac{d}{d n} (e^{(2 n + 3) l n (i)})

Apply the chain rule:

e^{(2 n + 3) l n (i)} \frac{d}{d n} ((2 n + 3) ln (i))

= e^{(2 n + 3) l n (i)} \frac{d}{d n} ((2 n + 3) ln (i))

\frac{d}{d n} ((2 n + 3) ln (i)) = 2 ln (i)

= e^{(2 n + 3) l n (i)} \cdot 2 ln (i)

e^{(2 n + 3) l n (i)} = i^{2 n + 3}

= 2 ln (i) i^{2 n + 3}

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