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y=sin³5x
The derivative of the function/ y=sin³5x

Derivative of y=sin³5x

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

The graph:

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The solution

You have entered [src] 
   35   
sin  (x)
sin⁡35(x)\sin^{35}{\left(x \right)} 
d /   35   \
--\sin  (x)/
dx
ddxsin⁡35(x)\frac{d}{d x} \sin^{35}{\left(x \right)}
Transform
Detail solution

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

  2. Apply the power rule: u35u^{35} goes to 35u3435 u^{34}

  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:

    35sin⁡34(x)cos⁡(x)35 \sin^{34}{\left(x \right)} \cos{\left(x \right)}

The answer is:

35sin⁡34(x)cos⁡(x)35 \sin^{34}{\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] 
      34          
35*sin  (x)*cos(x)
35sin⁡34(x)cos⁡(x)35 \sin^{34}{\left(x \right)} \cos{\left(x \right)}
Simplify
The second derivative [src] 
      33    /     2            2   \
35*sin  (x)*\- sin (x) + 34*cos (x)/
35(−sin⁡2(x)+34cos⁡2(x))sin⁡33(x)35 \left(- \sin^{2}{\left(x \right)} + 34 \cos^{2}{\left(x \right)}\right) \sin^{33}{\left(x \right)}
Simplify
The third derivative [src] 
      32    /         2              2   \       
35*sin  (x)*\- 103*sin (x) + 1122*cos (x)/*cos(x)
35(−103sin⁡2(x)+1122cos⁡2(x))sin⁡32(x)cos⁡(x)35 \left(- 103 \sin^{2}{\left(x \right)} + 1122 \cos^{2}{\left(x \right)}\right) \sin^{32}{\left(x \right)} \cos{\left(x \right)}
Simplify
The graph
Derivative of y=sin³5x
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