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Derivative of:
Derivative of sin(4x)
Derivative of e^(sin(1-3*x)^(2))
Derivative of x*e^((-1)/x^3)
Derivative of (x+5)/(x-1)
Identical expressions
x^ three -2cos2x
x cubed minus 2 co sinus of e of 2x
x to the power of three minus 2 co sinus of e of 2x
x3-2cos2x
x³-2cos2x
x to the power of 3-2cos2x
Similar expressions
x^3+2cos2x

The derivative of the function/ x^3-2cos2x

Derivative of x^3-2cos2x

The solution

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 3             
x  - 2*cos(2*x)

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

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

Detail solution

Differentiate $x^{3} - 2 \cos{\left(2 x \right)}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. 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: $4 \sin{\left(2 x \right)}$
The result is: $3 x^{2} + 4 \sin{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

2*(3 - 8*sin(2*x))

$$2 \left(3 - 8 \sin{\left(2 x \right)}\right)$$

Simplify