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x-sin(x)
The derivative of the function/ x-sin(x)

Derivative of x-sin(x)

Function f() - derivative -N order at the point
v

The graph:

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The solution

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

  1. Differentiate x−sin⁡(x)x - \sin{\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. The derivative of sine is cosine:

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

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

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

The answer is:

1−cos⁡(x)1 - \cos{\left(x \right)}

The graph
02468-8-6-4-2-1010-2525
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1 - cos(x)
1−cos⁡(x)1 - \cos{\left(x \right)}
Simplify
The second derivative [src] 
sin(x)
sin⁡(x)\sin{\left(x \right)}
Simplify
The third derivative [src] 
cos(x)
cos⁡(x)\cos{\left(x \right)}
Simplify
The graph
Derivative of x-sin(x)
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