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Popular >

d/(dn)((sqrt(-i))^{4n})

Solution

\frac{d}{d n} ((- i)^{4 n})

Solution

2 ln (- i) (- i)^{2 n}

Solution steps

\frac{d}{d n} ((- i)^{4 n})

Apply exponent rule:

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

(- i)^{4 n} = e^{4 n l n (- i)}

= \frac{d}{d n} (e^{4 n l n (- i)})

Apply the chain rule:

e^{4 n l n (- i)} \frac{d}{d n} (4 n ln (- i))

= e^{4 n l n (- i)} \frac{d}{d n} (4 n ln (- i))

\frac{d}{d n} (4 n ln (- i)) = 4 ln (- i)

= e^{4 n l n (- i)} \cdot 4 ln (- i)

Simplify

e^{4 n l n (- i)} \cdot 4 ln (- i) : 2 ln (- i) (- i)^{2 n}

= 2 ln (- i) (- i)^{2 n}

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Frequently Asked Questions (FAQ)

What is the d/(dn)((sqrt(-i))^{4n}) ?
The d/(dn)((sqrt(-i))^{4n}) is 2ln(-i)(-i)^{2n}
What is the first d/(dn)((sqrt(-i))^{4n}) ?
The first d/(dn)((sqrt(-i))^{4n}) is 2ln(-i)(-i)^{2n}