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

Derivative of 2x-sin(3x)

The solution

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2*x - sin(3*x)

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

d                 
--(2*x - sin(3*x))
dx

$$\frac{d}{d x} \left(2 x - \sin{\left(3 x \right)}\right)$$

Transform

Detail solution

Differentiate $2 x - \sin{\left(3 x \right)}$ 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: $2$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 3 x$ .
  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 $\frac{d}{d x} 3 x$ :
    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: $3$
    The result of the chain rule is:
    
    $3 \cos{\left(3 x \right)}$
  So, the result is: $- 3 \cos{\left(3 x \right)}$
The result is: $2 - 3 \cos{\left(3 x \right)}$

The answer is:

$2 - 3 \cos{\left(3 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2 - 3*cos(3*x)

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

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

The graph

Derivative of 2*x-sin(3*x)