Detail solution
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Rewrite the function to be differentiated:
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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]
$$\tan{\left(x \right)} \sec{\left(x \right)}$$
The second derivative
[src]
/ 2 \
\1 + 2*tan (x)/*sec(x)
$$\left(2 \tan^{2}{\left(x \right)} + 1\right) \sec{\left(x \right)}$$
The third derivative
[src]
/ 2 \
\5 + 6*tan (x)/*sec(x)*tan(x)
$$\left(6 \tan^{2}{\left(x \right)} + 5\right) \tan{\left(x \right)} \sec{\left(x \right)}$$