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The derivative of the function/ cos(k*x^63)

Derivative of cos(k*x^63)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   63\
cos\k*x  /
$$\cos{\left(k x^{63} \right)}$$ 
cos(k*x^63)
Detail solution

  1. Let .

  2. The derivative of cosine is negative sine:

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

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result of the chain rule is:

The answer is:

The first derivative [src] 
       62    /   63\
-63*k*x  *sin\k*x  /
$$- 63 k x^{62} \sin{\left(k x^{63} \right)}$$
Simplify
The second derivative [src] 
       61 /      /   63\         63    /   63\\
-63*k*x  *\62*sin\k*x  / + 63*k*x  *cos\k*x  //
$$- 63 k x^{61} \left(63 k x^{63} \cos{\left(k x^{63} \right)} + 62 \sin{\left(k x^{63} \right)}\right)$$
Simplify
The third derivative [src] 
      60 /          /   63\            63    /   63\         2  126    /   63\\
63*k*x  *\- 3782*sin\k*x  / - 11718*k*x  *cos\k*x  / + 3969*k *x   *sin\k*x  //
$$63 k x^{60} \left(3969 k^{2} x^{126} \sin{\left(k x^{63} \right)} - 11718 k x^{63} \cos{\left(k x^{63} \right)} - 3782 \sin{\left(k x^{63} \right)}\right)$$
Simplify
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