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cossin^2(x)

Derivative of cossin^2(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2        
cos (sin(x))
$$\cos^{2}{\left(\sin{\left(x \right)} \right)}$$
d /   2        \
--\cos (sin(x))/
dx              
$$\frac{d}{d x} \cos^{2}{\left(\sin{\left(x \right)} \right)}$$
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. The derivative of cosine is negative sine:

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
-2*cos(x)*cos(sin(x))*sin(sin(x))
$$- 2 \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}$$
The second derivative [src]
  /   2       2              2       2                                         \
2*\cos (x)*sin (sin(x)) - cos (x)*cos (sin(x)) + cos(sin(x))*sin(x)*sin(sin(x))/
$$2 \left(\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(x \right)} \right)} + \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} \cos^{2}{\left(\sin{\left(x \right)} \right)}\right)$$
The third derivative [src]
  /                               2                       2                       2                           \       
2*\cos(sin(x))*sin(sin(x)) - 3*sin (sin(x))*sin(x) + 3*cos (sin(x))*sin(x) + 4*cos (x)*cos(sin(x))*sin(sin(x))/*cos(x)
$$2 \left(- 3 \sin{\left(x \right)} \sin^{2}{\left(\sin{\left(x \right)} \right)} + 3 \sin{\left(x \right)} \cos^{2}{\left(\sin{\left(x \right)} \right)} + 4 \sin{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(x \right)} \right)}\right) \cos{\left(x \right)}$$
The graph
Derivative of cossin^2(x)