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Derivative of:
Derivative of e^x^x
Derivative of 5e^x
Derivative of 4-2x
Derivative of 3*(2-x)^6
Identical expressions
x- two *sin^2x
x minus 2 multiply by sinus of squared x
x minus two multiply by sinus of squared x
x-2*sin2x
x-2*sin²x
x-2*sin to the power of 2x
x-2sin^2x
x-2sin2x
Similar expressions
x+2*sin^2x

The derivative of the function/ x-2*sin^2x

Derivative of x-2*sin^2x

The solution

You have entered [src]

         2   
x - 2*sin (x)

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

x - 2*sin(x)^2

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1 - 4*cos(x)*sin(x)

$$- 4 \sin{\left(x \right)} \cos{\left(x \right)} + 1$$

Simplify

The second derivative [src]

  /   2         2   \
4*\sin (x) - cos (x)/

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

Simplify

The third derivative [src]

16*cos(x)*sin(x)

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

Simplify