Detail solution
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Let .
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Then, apply the chain rule. Multiply by :
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Apply the power rule: goes to
The result of the chain rule is:
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Now simplify:
The answer is:
The first derivative
[src]
$$2 \cdot 2^{x^{2}} x \log{\left(2 \right)}$$
The second derivative
[src]
/ 2\
\x / / 2 \
2*2 *\1 + 2*x *log(2)/*log(2)
$$2 \cdot 2^{x^{2}} \cdot \left(2 x^{2} \log{\left(2 \right)} + 1\right) \log{\left(2 \right)}$$
The third derivative
[src]
/ 2\
\x / 2 / 2 \
4*x*2 *log (2)*\3 + 2*x *log(2)/
$$4 \cdot 2^{x^{2}} x \left(2 x^{2} \log{\left(2 \right)} + 3\right) \log{\left(2 \right)}^{2}$$