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The derivative of the function/ sin²*x³

Derivative of sin²*x³

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        / 3\
        \2 /
(sin(x))
$$\sin^{2^{3}}{\left(x \right)}$$ 
  /        / 3\\
d |        \2 /|
--\(sin(x))    /
dx
$$\frac{d}{d x} \sin^{2^{3}}{\left(x \right)}$$
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:

  4. Now simplify:

The answer is:

The first derivative [src] 
          / 3\       
          \2 /       
8*(sin(x))    *cos(x)
---------------------
        sin(x)
$$\frac{8 \sin^{2^{3}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}$$
Simplify
The second derivative [src] 
     6    /     2           2   \
8*sin (x)*\- sin (x) + 7*cos (x)/
$$8 \left(- \sin^{2}{\left(x \right)} + 7 \cos^{2}{\left(x \right)}\right) \sin^{6}{\left(x \right)}$$
Simplify
The third derivative [src] 
      5    /        2            2   \       
16*sin (x)*\- 11*sin (x) + 21*cos (x)/*cos(x)
$$16 \left(- 11 \sin^{2}{\left(x \right)} + 21 \cos^{2}{\left(x \right)}\right) \sin^{5}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
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