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

Derivative of x-2*sin^2x

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
         2   
x - 2*sin (x)
x−2sin⁡2(x)x - 2 \sin^{2}{\left(x \right)} 
x - 2*sin(x)^2
Detail solution

  1. Differentiate x−2sin⁡2(x)x - 2 \sin^{2}{\left(x \right)} term by term:

    1. Apply the power rule: xx goes to 11

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let u=sin⁡(x)u = \sin{\left(x \right)}.

      2. Apply the power rule: u2u^{2} goes to 2u2 u

      3. Then, apply the chain rule. Multiply by ddxsin⁡(x)\frac{d}{d x} \sin{\left(x \right)}:

        1. The derivative of sine is cosine:

          ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

        The result of the chain rule is:

        2sin⁡(x)cos⁡(x)2 \sin{\left(x \right)} \cos{\left(x \right)}

      So, the result is: −4sin⁡(x)cos⁡(x)- 4 \sin{\left(x \right)} \cos{\left(x \right)}

    The result is: −4sin⁡(x)cos⁡(x)+1- 4 \sin{\left(x \right)} \cos{\left(x \right)} + 1

  2. Now simplify:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1 - 4*cos(x)*sin(x)
−4sin⁡(x)cos⁡(x)+1- 4 \sin{\left(x \right)} \cos{\left(x \right)} + 1
Simplify
The second derivative [src] 
  /   2         2   \
4*\sin (x) - cos (x)/
4(sin⁡2(x)−cos⁡2(x))4 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)
Simplify
The third derivative [src] 
16*cos(x)*sin(x)
16sin⁡(x)cos⁡(x)16 \sin{\left(x \right)} \cos{\left(x \right)}
Simplify
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