Detail solution
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Let .
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Apply the power rule: goes to
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Then, apply the chain rule. Multiply by :
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Let .
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Apply the power rule: goes to
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Then, apply the chain rule. Multiply by :
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The derivative of cosine is negative sine:
The result of the chain rule is:
The result of the chain rule is:
The answer is:
The first derivative
[src]
2*sin(y)
--------------
2
cos(y)*cos (y)
$$\frac{2 \sin{\left(y \right)}}{\cos{\left(y \right)} \cos^{2}{\left(y \right)}}$$
The second derivative
[src]
/ 2 \
| 3*sin (y)|
2*|1 + ---------|
| 2 |
\ cos (y) /
-----------------
2
cos (y)
$$\frac{2 \left(\frac{3 \sin^{2}{\left(y \right)}}{\cos^{2}{\left(y \right)}} + 1\right)}{\cos^{2}{\left(y \right)}}$$
The third derivative
[src]
/ 2 \
| 3*sin (y)|
8*|2 + ---------|*sin(y)
| 2 |
\ cos (y) /
------------------------
3
cos (y)
$$\frac{8 \left(\frac{3 \sin^{2}{\left(y \right)}}{\cos^{2}{\left(y \right)}} + 2\right) \sin{\left(y \right)}}{\cos^{3}{\left(y \right)}}$$