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 cosine is negative sine:
The result of the chain rule is:
The answer is:
The first derivative
[src]
$$- 6 \sin{\left(x \right)} \cos^{5}{\left(x \right)}$$
The second derivative
[src]
4 / 2 2 \
6*cos (x)*\- cos (x) + 5*sin (x)/
$$6 \left(5 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos^{4}{\left(x \right)}$$
The third derivative
[src]
3 / 2 2 \
24*cos (x)*\- 5*sin (x) + 4*cos (x)/*sin(x)
$$24 \left(- 5 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos^{3}{\left(x \right)}$$