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Derivative of:
Derivative of e^(2-x)
Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
Derivative of cos(3*x)^(2)-sin(3*x)^(2)
Derivative of a^2
Graphing y =:
2*cos(2*x)-3*x
Identical expressions
two *cos(two *x)- three *x
2 multiply by co sinus of e of (2 multiply by x) minus 3 multiply by x
two multiply by co sinus of e of (two multiply by x) minus three multiply by x
2cos(2x)-3x
2cos2x-3x
Similar expressions
2*cos(2*x)+3*x

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

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

The solution

You have entered [src]

2*cos(2*x) - 3*x

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

2*cos(2*x) - 3*x

Detail solution

Differentiate $- 3 x + 2 \cos{\left(2 x \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 2 x$ .
  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 $\frac{d}{d x} 2 x$ :
    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:
    
    $- 2 \sin{\left(2 x \right)}$
  So, the result is: $- 4 \sin{\left(2 x \right)}$
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: $-3$
The result is: $- 4 \sin{\left(2 x \right)} - 3$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3 - 4*sin(2*x)

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

Simplify

The second derivative [src]

-8*cos(2*x)

$$- 8 \cos{\left(2 x \right)}$$

Simplify

The third derivative [src]

16*sin(2*x)

$$16 \sin{\left(2 x \right)}$$

Simplify