Detail solution
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Let .
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The derivative of is .
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Then, apply the chain rule. Multiply by :
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The derivative of sine is cosine:
The result of the chain rule is:
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Now simplify:
The answer is:
The first derivative
[src]
$$\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
The second derivative
[src]
/ 2 \
| cos (x)|
-|1 + -------|
| 2 |
\ sin (x)/
$$- (1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}})$$
The third derivative
[src]
/ 2 \
| cos (x)|
2*|1 + -------|*cos(x)
| 2 |
\ sin (x)/
----------------------
sin(x)
$$\frac{2 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}}$$