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sin(x)*sin(x)*sin(x)

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sinx*sinx*sinx

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

Derivative of sin(x)sin(x)sin(x)

The solution

You have entered [src]

sin(x)*sin(x)*sin(x)

$$\sin{\left(x \right)} \sin{\left(x \right)} \sin{\left(x \right)}$$

(sin(x)*sin(x))*sin(x)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = \sin{\left(x \right)} \sin{\left(x \right)}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  $g{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  The result is: $2 \sin{\left(x \right)} \cos{\left(x \right)}$
$g{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
The result is: $3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}$

The answer is:

$3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2          
3*sin (x)*cos(x)

$$3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

/       2           2   \       
\- 3*sin (x) + 6*cos (x)/*sin(x)

$$\left(- 3 \sin^{2}{\left(x \right)} + 6 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}$$

Simplify

The third derivative [src]

   /       2           2   \       
-3*\- 2*cos (x) + 7*sin (x)/*cos(x)

$$- 3 \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}$$

Simplify

The graph

Derivative of sin(x)*sin(x)*sin(x)