What is the derivative of cot(sqrt(x^2+pix)) ?

The derivative of cot(sqrt(x^2+pix)) is -(csc^2(sqrt(x^2+pix))(2x+pi))/(2sqrt(x^2+pix))

What is the first derivative of cot(sqrt(x^2+pix)) ?

The first derivative of cot(sqrt(x^2+pix)) is -(csc^2(sqrt(x^2+pix))(2x+pi))/(2sqrt(x^2+pix))

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derivative of

cot (x^{2} + π x)

- \frac{csc ^{2} ( x ^{2} + π x ) ( 2 x + π )}{2 x ^{2} + π x}

Solution steps

\frac{d}{d x} (cot (x^{2} + π x))

Apply the chain rule:

- csc^{2} (x^{2} + π x) \frac{d}{d x} (x^{2} + π x)

= - csc^{2} (x^{2} + π x) \frac{d}{d x} (x^{2} + π x)

\frac{d}{d x} (x^{2} + π x) = \frac{2 x + π}{2 x ^{2} + π x}

= - csc^{2} (x^{2} + π x) \frac{2 x + π}{2 x ^{2} + π x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{csc ^{2} ( x ^{2} + π x ) ( 2 x + π )}{2 x ^{2} + π x}

\frac{s + 1}{( s ^{2} + 2 ) ( s + 1 )}

9 sin (2 x)

f (x) = \frac{x}{4 + x ^{2}}

(4^{x})^{^{'}}

n = 1 \sum \infty ln (\frac{n}{n + 1})

What is the derivative of cot(sqrt(x^2+pix)) ?
The derivative of cot(sqrt(x^2+pix)) is -(csc^2(sqrt(x^2+pix))(2x+pi))/(2sqrt(x^2+pix))
What is the first derivative of cot(sqrt(x^2+pix)) ?
The first derivative of cot(sqrt(x^2+pix)) is -(csc^2(sqrt(x^2+pix))(2x+pi))/(2sqrt(x^2+pix))