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Derivative of (5sin10x-3)/100

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
5*sin(10*x) - 3
---------------
      100      
$$\frac{5 \sin{\left(10 x \right)} - 3}{100}$$
(5*sin(10*x) - 3)/100
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Differentiate term by term:

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

        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:

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
cos(10*x)
---------
    2    
$$\frac{\cos{\left(10 x \right)}}{2}$$
The second derivative [src]
-5*sin(10*x)
$$- 5 \sin{\left(10 x \right)}$$
The third derivative [src]
-50*cos(10*x)
$$- 50 \cos{\left(10 x \right)}$$