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y=sin²x³
The derivative of the function/ y=sin²x³

Derivative of y=sin²x³

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

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The solution

You have entered [src] 
   8   
sin (x)
sin⁡8(x)\sin^{8}{\left(x \right)} 
sin(x)^8
Detail solution

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

  2. Apply the power rule: u8u^{8} goes to 8u78 u^{7}

  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:

    8sin⁡7(x)cos⁡(x)8 \sin^{7}{\left(x \right)} \cos{\left(x \right)}

The answer is:

8sin⁡7(x)cos⁡(x)8 \sin^{7}{\left(x \right)} \cos{\left(x \right)}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     7          
8*sin (x)*cos(x)
8sin⁡7(x)cos⁡(x)8 \sin^{7}{\left(x \right)} \cos{\left(x \right)}
Simplify
The second derivative [src] 
     6    /     2           2   \
8*sin (x)*\- sin (x) + 7*cos (x)/
8(−sin⁡2(x)+7cos⁡2(x))sin⁡6(x)8 \left(- \sin^{2}{\left(x \right)} + 7 \cos^{2}{\left(x \right)}\right) \sin^{6}{\left(x \right)}
Simplify
The third derivative [src] 
      5    /        2            2   \       
16*sin (x)*\- 11*sin (x) + 21*cos (x)/*cos(x)
16(−11sin⁡2(x)+21cos⁡2(x))sin⁡5(x)cos⁡(x)16 \left(- 11 \sin^{2}{\left(x \right)} + 21 \cos^{2}{\left(x \right)}\right) \sin^{5}{\left(x \right)} \cos{\left(x \right)}
Simplify
The graph
Derivative of y=sin²x³
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