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2*sin(x)*(cos(x)+1)

Derivative of 2*sin(x)*(cos(x)+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
2*sin(x)*(cos(x) + 1)
$$\left(\cos{\left(x \right)} + 1\right) 2 \sin{\left(x \right)}$$
(2*sin(x))*(cos(x) + 1)
Detail solution
  1. Apply the product rule:

    ; to find :

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

      1. The derivative of sine is cosine:

      So, the result is:

    ; to find :

    1. Differentiate term by term:

      1. The derivative of cosine is negative sine:

      2. The derivative of the constant is zero.

      The result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       2                           
- 2*sin (x) + 2*(cos(x) + 1)*cos(x)
$$2 \left(\cos{\left(x \right)} + 1\right) \cos{\left(x \right)} - 2 \sin^{2}{\left(x \right)}$$
The second derivative [src]
-2*(1 + 4*cos(x))*sin(x)
$$- 2 \left(4 \cos{\left(x \right)} + 1\right) \sin{\left(x \right)}$$
The third derivative [src]
  /       2           2                         \
2*\- 3*cos (x) + 4*sin (x) - (1 + cos(x))*cos(x)/
$$2 \left(- \left(\cos{\left(x \right)} + 1\right) \cos{\left(x \right)} + 4 \sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right)$$
The graph
Derivative of 2*sin(x)*(cos(x)+1)