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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The derivative of is .
The result of the chain rule is:
The answer is:
The first derivative
[src]
$$\frac{5 \log{\left(x \right)}^{4}}{x}$$
The second derivative
[src]
3
5*log (x)*(4 - log(x))
----------------------
2
x
$$\frac{5 \left(4 - \log{\left(x \right)}\right) \log{\left(x \right)}^{3}}{x^{2}}$$
The third derivative
[src]
2 / 2 \
10*log (x)*\6 + log (x) - 6*log(x)/
-----------------------------------
3
x
$$\frac{10 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \log{\left(x \right)}^{2}}{x^{3}}$$