Mister Exam

Derivative of sin(x)*sin(x)

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

The graph:

from to

Piecewise:

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)}
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
The first derivative [src]
2*cos(x)*sin(x)
2sin(x)cos(x)2 \sin{\left(x \right)} \cos{\left(x \right)}
The second derivative [src]
  /   2         2   \
2*\cos (x) - sin (x)/
2(sin2(x)+cos2(x))2 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)
The third derivative [src]
-8*cos(x)*sin(x)
8sin(x)cos(x)- 8 \sin{\left(x \right)} \cos{\left(x \right)}
The graph
Derivative of sin(x)*sin(x)