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Derivative of:
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Derivative of -3*x^3+2*x^2-x-5
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Identical expressions
sin(three *x- two *pi)+pi
sinus of (3 multiply by x minus 2 multiply by Pi ) plus Pi
sinus of (three multiply by x minus two multiply by Pi ) plus Pi
sin(3x-2pi)+pi
sin3x-2pi+pi
Similar expressions
sin(3*x-2*pi)-pi
sin(3*x+2*pi)+pi

The derivative of the function/ sin(3*x-2*pi)+pi

Derivative of sin(3x-2pi)+pi

The solution

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sin(3*x - 2*pi) + pi

$$\sin{\left(3 x - 2 \pi \right)} + \pi$$

sin(3*x - 2*pi) + pi

Detail solution

Differentiate $\sin{\left(3 x - 2 \pi \right)} + \pi$ term by term:
1. Let $u = 3 x - 2 \pi$ .
2. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x - 2 \pi\right)$ :
  1. Differentiate $3 x - 2 \pi$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $3$
    2. The derivative of the constant $- 2 \pi$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $3 \cos{\left(3 x \right)}$
4. The derivative of the constant $\pi$ is zero.
The result is: $3 \cos{\left(3 x \right)}$

The answer is:

$3 \cos{\left(3 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3*cos(3*x)

$$3 \cos{\left(3 x \right)}$$

Simplify

The second derivative [src]

-9*sin(3*x)

$$- 9 \sin{\left(3 x \right)}$$

Simplify

The third derivative [src]

-27*cos(3*x)

$$- 27 \cos{\left(3 x \right)}$$

Simplify