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y=sin5x-1/3sin³5x

Derivative of y=sin5x-1/3sin³5x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
              35   
           sin  (x)
sin(5*x) - --------
              3    
$$- \frac{\sin^{35}{\left(x \right)}}{3} + \sin{\left(5 x \right)}$$
  /              35   \
d |           sin  (x)|
--|sin(5*x) - --------|
dx\              3    /
$$\frac{d}{d x} \left(- \frac{\sin^{35}{\left(x \right)}}{3} + \sin{\left(5 x \right)}\right)$$
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of sine is cosine:

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Let .

        2. Apply the power rule: goes to

        3. Then, apply the chain rule. Multiply by :

          1. The derivative of sine is cosine:

          The result of the chain rule is:

        So, the result is:

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
                   34          
             35*sin  (x)*cos(x)
5*cos(5*x) - ------------------
                     3         
$$- \frac{35 \sin^{34}{\left(x \right)} \cos{\left(x \right)}}{3} + 5 \cos{\left(5 x \right)}$$
The second derivative [src]
  /                   35             2       33   \
  |              7*sin  (x)   238*cos (x)*sin  (x)|
5*|-5*sin(5*x) + ---------- - --------------------|
  \                  3                 3          /
$$5 \cdot \left(\frac{7 \sin^{35}{\left(x \right)}}{3} - \frac{238 \sin^{33}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - 5 \sin{\left(5 x \right)}\right)$$
The third derivative [src]
  /                                              34          \
  |                       3       32      721*sin  (x)*cos(x)|
5*|-25*cos(5*x) - 2618*cos (x)*sin  (x) + -------------------|
  \                                                3         /
$$5 \cdot \left(\frac{721 \sin^{34}{\left(x \right)} \cos{\left(x \right)}}{3} - 2618 \sin^{32}{\left(x \right)} \cos^{3}{\left(x \right)} - 25 \cos{\left(5 x \right)}\right)$$
The graph
Derivative of y=sin5x-1/3sin³5x