Detail solution
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Let .
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The derivative of sine is cosine:
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Then, apply the chain rule. Multiply by :
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
The answer is:
The first derivative
[src]
$$4 x \cos{\left(2 x^{2} \right)}$$
The second derivative
[src]
/ 2 / 2\ / 2\\
4*\- 4*x *sin\2*x / + cos\2*x //
$$4 \left(- 4 x^{2} \sin{\left(2 x^{2} \right)} + \cos{\left(2 x^{2} \right)}\right)$$
The third derivative
[src]
/ / 2\ 2 / 2\\
-16*x*\3*sin\2*x / + 4*x *cos\2*x //
$$- 16 x \left(4 x^{2} \cos{\left(2 x^{2} \right)} + 3 \sin{\left(2 x^{2} \right)}\right)$$