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Derivative of:
Derivative of atan(sqrt(x))
Derivative of 3*x^5
Derivative of 3*x^2*e^x
Derivative of 3*cos(3*x)
Identical expressions
four *cos(two *x)- five
4 multiply by co sinus of e of (2 multiply by x) minus 5
four multiply by co sinus of e of (two multiply by x) minus five
4cos(2x)-5
4cos2x-5
Similar expressions
4*cos(2*x)+5

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

Derivative of 4cos(2x)-5

The solution

You have entered [src]

4*cos(2*x) - 5

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

4*cos(2*x) - 5

Detail solution

Differentiate $4 \cos{\left(2 x \right)} - 5$ 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: $- 8 \sin{\left(2 x \right)}$
2. The derivative of the constant $-5$ is zero.
The result is: $- 8 \sin{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-8*sin(2*x)

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

Simplify

The second derivative [src]

-16*cos(2*x)

$$- 16 \cos{\left(2 x \right)}$$

Simplify

The third derivative [src]

32*sin(2*x)

$$32 \sin{\left(2 x \right)}$$

Simplify