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sin(sin(x))
The derivative of the function/ sin(sin(x))

Derivative of sin(sin(x))

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
sin(sin(x))
sin⁡(sin⁡(x))\sin{\left(\sin{\left(x \right)} \right)} 
sin(sin(x))
Detail solution

  1. Let u=sin⁡(x)u = \sin{\left(x \right)}.

  2. The derivative of sine is cosine:

    ddusin⁡(u)=cos⁡(u)\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}

  3. Then, apply the chain rule. Multiply by ddxsin⁡(x)\frac{d}{d x} \sin{\left(x \right)}:

    1. The derivative of sine is cosine:

      ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

    The result of the chain rule is:

    cos⁡(x)cos⁡(sin⁡(x))\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}

The answer is:

cos⁡(x)cos⁡(sin⁡(x))\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
cos(x)*cos(sin(x))
cos⁡(x)cos⁡(sin⁡(x))\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}
Simplify
The second derivative [src] 
 /   2                                    \
-\cos (x)*sin(sin(x)) + cos(sin(x))*sin(x)/
−(sin⁡(x)cos⁡(sin⁡(x))+sin⁡(sin⁡(x))cos⁡2(x))- (\sin{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} + \sin{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)})
Simplify
The third derivative [src] 
/                  2                                      \       
\-cos(sin(x)) - cos (x)*cos(sin(x)) + 3*sin(x)*sin(sin(x))/*cos(x)
(3sin⁡(x)sin⁡(sin⁡(x))−cos⁡2(x)cos⁡(sin⁡(x))−cos⁡(sin⁡(x)))cos⁡(x)\left(3 \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} - \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} - \cos{\left(\sin{\left(x \right)} \right)}\right) \cos{\left(x \right)}
Simplify
The graph
Derivative of sin(sin(x))
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