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sin(x)*sin(x)
The derivative of the function/ sin(x)*sin(x)

Derivative of sin(x)*sin(x)

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] 
sin(x)*sin(x)
sin⁡(x)sin⁡(x)\sin{\left(x \right)} \sin{\left(x \right)} 
d                
--(sin(x)*sin(x))
dx
ddxsin⁡(x)sin⁡(x)\frac{d}{d x} \sin{\left(x \right)} \sin{\left(x \right)}
Transform
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=sin⁡(x)f{\left(x \right)} = \sin{\left(x \right)}; to find ddxf(x)\frac{d}{d x} f{\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)}

    g(x)=sin⁡(x)g{\left(x \right)} = \sin{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\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 is: 2sin⁡(x)cos⁡(x)2 \sin{\left(x \right)} \cos{\left(x \right)}

  2. 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 sin(x)*sin(x)
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