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sinx^2
The derivative of the function/ sinx^2

Derivative of sinx^2

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

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from to

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The solution

You have entered [src] 
   2   
sin (x)
sin⁡2(x)\sin^{2}{\left(x \right)} 
sin(x)^2
Detail solution

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

  2. Apply the power rule: u2u^{2} goes to 2u2 u

  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:

    2sin⁡(x)cos⁡(x)2 \sin{\left(x \right)} \cos{\left(x \right)}

  4. Now simplify:

    sin⁡(2x)\sin{\left(2 x \right)}

The answer is:

sin⁡(2x)\sin{\left(2 x \right)}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2*cos(x)*sin(x)
2sin⁡(x)cos⁡(x)2 \sin{\left(x \right)} \cos{\left(x \right)}
Simplify
The second derivative [src] 
  /   2         2   \
2*\cos (x) - sin (x)/
2(−sin⁡2(x)+cos⁡2(x))2 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)
Simplify
The third derivative [src] 
-8*cos(x)*sin(x)
−8sin⁡(x)cos⁡(x)- 8 \sin{\left(x \right)} \cos{\left(x \right)}
Simplify
The graph
Derivative of sinx^2
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