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sin²2x
The derivative of the function/ sin²2x

Derivative of sin²2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   22   
sin  (x)
sin⁡22(x)\sin^{22}{\left(x \right)} 
d /   22   \
--\sin  (x)/
dx
ddxsin⁡22(x)\frac{d}{d x} \sin^{22}{\left(x \right)}
Transform
Detail solution

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

  2. Apply the power rule: u22u^{22} goes to 22u2122 u^{21}

  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:

    22sin⁡21(x)cos⁡(x)22 \sin^{21}{\left(x \right)} \cos{\left(x \right)}

The answer is:

22sin⁡21(x)cos⁡(x)22 \sin^{21}{\left(x \right)} \cos{\left(x \right)}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      21          
22*sin  (x)*cos(x)
22sin⁡21(x)cos⁡(x)22 \sin^{21}{\left(x \right)} \cos{\left(x \right)}
Simplify
The second derivative [src] 
      20    /     2            2   \
22*sin  (x)*\- sin (x) + 21*cos (x)/
22(−sin⁡2(x)+21cos⁡2(x))sin⁡20(x)22 \left(- \sin^{2}{\left(x \right)} + 21 \cos^{2}{\left(x \right)}\right) \sin^{20}{\left(x \right)}
Simplify
The third derivative [src] 
      19    /        2             2   \       
88*sin  (x)*\- 16*sin (x) + 105*cos (x)/*cos(x)
88(−16sin⁡2(x)+105cos⁡2(x))sin⁡19(x)cos⁡(x)88 \left(- 16 \sin^{2}{\left(x \right)} + 105 \cos^{2}{\left(x \right)}\right) \sin^{19}{\left(x \right)} \cos{\left(x \right)}
Simplify
The graph
Derivative of sin²2x
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