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sin(5*x)^(6)

Derivative of sin(5*x)^(6)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   6     
sin (5*x)
$$\sin^{6}{\left(5 x \right)}$$
d /   6     \
--\sin (5*x)/
dx           
$$\frac{d}{d x} \sin^{6}{\left(5 x \right)}$$
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 sine is cosine:

    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 result of the chain rule is:


The answer is:

The graph
The first derivative [src]
      5              
30*sin (5*x)*cos(5*x)
$$30 \sin^{5}{\left(5 x \right)} \cos{\left(5 x \right)}$$
The second derivative [src]
       4      /     2             2     \
150*sin (5*x)*\- sin (5*x) + 5*cos (5*x)/
$$150 \left(- \sin^{2}{\left(5 x \right)} + 5 \cos^{2}{\left(5 x \right)}\right) \sin^{4}{\left(5 x \right)}$$
The third derivative [src]
        3      /       2             2     \         
3000*sin (5*x)*\- 4*sin (5*x) + 5*cos (5*x)/*cos(5*x)
$$3000 \left(- 4 \sin^{2}{\left(5 x \right)} + 5 \cos^{2}{\left(5 x \right)}\right) \sin^{3}{\left(5 x \right)} \cos{\left(5 x \right)}$$
The graph
Derivative of sin(5*x)^(6)