Detail solution
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Let .
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The derivative of is itself.
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Then, apply the chain rule. Multiply by :
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The derivative of sine is cosine:
The result of the chain rule is:
The answer is:
The first derivative
[src]
$$e^{\sin{\left(x \right)}} \cos{\left(x \right)}$$
The second derivative
[src]
/ 2 \ sin(x)
\cos (x) - sin(x)/*e
$$\left(- \sin{\left(x \right)} + \cos^{2}{\left(x \right)}\right) e^{\sin{\left(x \right)}}$$
The third derivative
[src]
/ 2 \ sin(x)
\-1 + cos (x) - 3*sin(x)/*cos(x)*e
$$\left(- 3 \sin{\left(x \right)} + \cos^{2}{\left(x \right)} - 1\right) e^{\sin{\left(x \right)}} \cos{\left(x \right)}$$