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2sin(2x)+(3+3cos4x)

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Derivative of:
Derivative of x/5
Derivative of x^2-4
Derivative of e^(x*(-2))
Derivative of -2x
Identical expressions
2sin(2x)+(three +3cos4x)
2 sinus of (2x) plus (3 plus 3 co sinus of e of 4x)
2 sinus of (2x) plus (three plus 3 co sinus of e of 4x)
2sin2x+3+3cos4x
Similar expressions
2sin(2x)-(3+3cos4x)
2sin(2x)+(3-3cos4x)

The derivative of the function/ 2sin(2x)+(3+3cos4x)

Derivative of 2sin(2x)+(3+3cos4x)

The solution

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2*sin(2*x) + 3 + 3*cos(4*x)

$$2 \sin{\left(2 x \right)} + 3 \cos{\left(4 x \right)} + 3$$

d                              
--(2*sin(2*x) + 3 + 3*cos(4*x))
dx

$$\frac{d}{d x} \left(2 \sin{\left(2 x \right)} + 3 \cos{\left(4 x \right)} + 3\right)$$

Transform

Detail solution

Differentiate $2 \sin{\left(2 x \right)} + 3 \cos{\left(4 x \right)} + 3$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 2 x$ .
  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 $\frac{d}{d x} 2 x$ :
    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: $2$
    The result of the chain rule is:
    
    $2 \cos{\left(2 x \right)}$
  So, the result is: $4 \cos{\left(2 x \right)}$
2. The derivative of the constant $3$ is zero.
3. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 4 x$ .
  2. The derivative of cosine is negative sine:
    
    $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 4 x$ :
    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: $4$
    The result of the chain rule is:
    
    $- 4 \sin{\left(4 x \right)}$
  So, the result is: $- 12 \sin{\left(4 x \right)}$
The result is: $- 12 \sin{\left(4 x \right)} + 4 \cos{\left(2 x \right)}$

The answer is:

$- 12 \sin{\left(4 x \right)} + 4 \cos{\left(2 x \right)}$

The graph

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The first derivative [src]

-12*sin(4*x) + 4*cos(2*x)

$$- 12 \sin{\left(4 x \right)} + 4 \cos{\left(2 x \right)}$$

Simplify

The second derivative [src]

-8*(6*cos(4*x) + sin(2*x))

$$- 8 \left(\sin{\left(2 x \right)} + 6 \cos{\left(4 x \right)}\right)$$

Simplify

3-th derivative [src]

16*(-cos(2*x) + 12*sin(4*x))

$$16 \cdot \left(12 \sin{\left(4 x \right)} - \cos{\left(2 x \right)}\right)$$

Simplify

The third derivative [src]

16*(-cos(2*x) + 12*sin(4*x))

$$16 \cdot \left(12 \sin{\left(4 x \right)} - \cos{\left(2 x \right)}\right)$$

Simplify

The graph

Derivative of 2sin(2x)+(3+3cos4x)