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Derivative of:
Derivative of x^7*e^x
Derivative of (x-1)/(x+1)
Derivative of e^(x*(-3))
Derivative of x/sin(x)
Identical expressions
five *cos(4x+ two)+ nine
5 multiply by co sinus of e of (4x plus 2) plus 9
five multiply by co sinus of e of (4x plus two) plus nine
5cos(4x+2)+9
5cos4x+2+9
Similar expressions
5*cos(4x-2)+9
5*cos(4x+2)-9

The derivative of the function/ 5*cos(4x+2)+9

Derivative of 5*cos(4x+2)+9

The solution

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5*cos(4*x + 2) + 9

$$5 \cos{\left(4 x + 2 \right)} + 9$$

5*cos(4*x + 2) + 9

Detail solution

Differentiate $5 \cos{\left(4 x + 2 \right)} + 9$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 4 x + 2$ .
  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 $\frac{d}{d x} \left(4 x + 2\right)$ :
    1. Differentiate $4 x + 2$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $4$
      2. The derivative of the constant $2$ is zero.
      The result is: $4$
    The result of the chain rule is:
    
    $- 4 \sin{\left(4 x + 2 \right)}$
  So, the result is: $- 20 \sin{\left(4 x + 2 \right)}$
2. The derivative of the constant $9$ is zero.
The result is: $- 20 \sin{\left(4 x + 2 \right)}$
Now simplify:

$- 20 \sin{\left(4 x + 2 \right)}$

The answer is:

$- 20 \sin{\left(4 x + 2 \right)}$

The graph

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The first derivative [src]

-20*sin(4*x + 2)

$$- 20 \sin{\left(4 x + 2 \right)}$$

Simplify

The second derivative [src]

-80*cos(2*(1 + 2*x))

$$- 80 \cos{\left(2 \left(2 x + 1\right) \right)}$$

Simplify

The third derivative [src]

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

$$320 \sin{\left(2 \left(2 x + 1\right) \right)}$$

Simplify