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The derivative of the function/ sinx^4

Derivative of sinx^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   4   
sin (x)
$$\sin^{4}{\left(x \right)}$$ 
d /   4   \
--\sin (x)/
dx
$$\frac{d}{d x} \sin^{4}{\left(x \right)}$$
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 first derivative [src] 
     3          
4*sin (x)*cos(x)
$$4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
     2    /     2           2   \
4*sin (x)*\- sin (x) + 3*cos (x)/
$$4 \left(- \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}\right) \sin^{2}{\left(x \right)}$$
Simplify
The third derivative [src] 
  /       2           2   \              
8*\- 5*sin (x) + 3*cos (x)/*cos(x)*sin(x)
$$8 \left(- 5 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$
Simplify
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