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

Derivative of sin^4

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
   4   
sin (x)
sin⁡4(x)\sin^{4}{\left(x \right)} 
sin(x)^4
Detail solution

  1. Let u=sin⁡(x)u = \sin{\left(x \right)}.

  2. Apply the power rule: u4u^{4} goes to 4u34 u^{3}

  3. Then, apply the chain rule. Multiply by ddxsin⁡(x)\frac{d}{d x} \sin{\left(x \right)}:

    1. The derivative of sine is cosine:

      ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

    The result of the chain rule is:

    4sin⁡3(x)cos⁡(x)4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}

The answer is:

4sin⁡3(x)cos⁡(x)4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}

The graph
02468-8-6-4-2-10102.5-2.5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     3          
4*sin (x)*cos(x)
4sin⁡3(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(−sin⁡2(x)+3cos⁡2(x))sin⁡2(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(−5sin⁡2(x)+3cos⁡2(x))sin⁡(x)cos⁡(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
The graph
Derivative of sin^4
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