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Popular >

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

Solution

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

Solution

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}

Popular Examples

d/(dc)(1.8c+32)

\frac{d}{d c} (1.8 c + 32)

derivative of (x+2)/x derivative of

\frac{x + 2}{x}

derivative of 1/(e^2x)derivative of

\frac{1}{e ^{2} x}

derivative of 2arctan(x/2)derivative of

2 arctan (\frac{x}{2})

derivative of d(4x^{15})(8x^3)derivative of

d (4 x^{15}) (8 x^{3})

Frequently Asked Questions (FAQ)

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}