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Derivative of:
Derivative of x^2*sqrt(1-x^2)
Derivative of e^x*x^2
Derivative of (x+3)/(x-3)
Derivative of x^3/(x^2-4)
Identical expressions
three *sin(four *x)- eleven *x
3 multiply by sinus of (4 multiply by x) minus 11 multiply by x
three multiply by sinus of (four multiply by x) minus eleven multiply by x
3sin(4x)-11x
3sin4x-11x
Similar expressions
3*sin(4*x)+11*x

The derivative of the function/ 3*sin(4*x)-11*x

Derivative of 3sin(4x)-11*x

The solution

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3*sin(4*x) - 11*x

$$- 11 x + 3 \sin{\left(4 x \right)}$$

3*sin(4*x) - 11*x

Detail solution

Differentiate $- 11 x + 3 \sin{\left(4 x \right)}$ 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. 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 $\frac{d}{d x} 4 x$ :
    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:
    
    $4 \cos{\left(4 x \right)}$
  So, the result is: $12 \cos{\left(4 x \right)}$
2. 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: $-11$
The result is: $12 \cos{\left(4 x \right)} - 11$

The answer is:

$12 \cos{\left(4 x \right)} - 11$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-11 + 12*cos(4*x)

$$12 \cos{\left(4 x \right)} - 11$$

Simplify

The second derivative [src]

-48*sin(4*x)

$$- 48 \sin{\left(4 x \right)}$$

Simplify

The third derivative [src]

-192*cos(4*x)

$$- 192 \cos{\left(4 x \right)}$$

Simplify