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sin³x
The derivative of the function/ sin³x

Derivative of sin³x

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
   3   
sin (x)
sin⁡3(x)\sin^{3}{\left(x \right)} 
sin(x)^3
Detail solution

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

  2. Apply the power rule: u3u^{3} goes to 3u23 u^{2}

  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:

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

The answer is:

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

The graph
02468-8-6-4-2-10102.5-2.5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     2          
3*sin (x)*cos(x)
3sin⁡2(x)cos⁡(x)3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}
Simplify
The second derivative [src] 
  /     2           2   \       
3*\- sin (x) + 2*cos (x)/*sin(x)
3(−sin⁡2(x)+2cos⁡2(x))sin⁡(x)3 \left(- \sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}
Simplify
The third derivative [src] 
  /       2           2   \       
3*\- 7*sin (x) + 2*cos (x)/*cos(x)
3(−7sin⁡2(x)+2cos⁡2(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 sin³x
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