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