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sin^3x^4
The derivative of the function/ sin^3x^4

Derivative of sin^3x^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   81   
sin  (x)
$$\sin^{81}{\left(x \right)}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. The derivative of sine is cosine:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      80          
81*sin  (x)*cos(x)
$$81 \sin^{80}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
      79    /     2            2   \
81*sin  (x)*\- sin (x) + 80*cos (x)/
$$81 \left(- \sin^{2}{\left(x \right)} + 80 \cos^{2}{\left(x \right)}\right) \sin^{79}{\left(x \right)}$$
Simplify
The third derivative [src] 
      78    /         2              2   \       
81*sin  (x)*\- 241*sin (x) + 6320*cos (x)/*cos(x)
$$81 \left(- 241 \sin^{2}{\left(x \right)} + 6320 \cos^{2}{\left(x \right)}\right) \sin^{78}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The graph
Derivative of sin^3x^4
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