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

Derivative of sin(x)-cos(x)

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

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The solution

You have entered [src] 
sin(x) - cos(x)
sin⁡(x)−cos⁡(x)\sin{\left(x \right)} - \cos{\left(x \right)} 
d                  
--(sin(x) - cos(x))
dx
ddx(sin⁡(x)−cos⁡(x))\frac{d}{d x} \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)
Transform
Detail solution

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

    1. The derivative of sine is cosine:

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

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

      1. The derivative of cosine is negative sine:

        ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

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

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

The answer is:

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

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
cos(x) + sin(x)
sin⁡(x)+cos⁡(x)\sin{\left(x \right)} + \cos{\left(x \right)}
Simplify
The second derivative [src] 
-sin(x) + cos(x)
−sin⁡(x)+cos⁡(x)- \sin{\left(x \right)} + \cos{\left(x \right)}
Simplify
The third derivative [src] 
-(cos(x) + sin(x))
−(sin⁡(x)+cos⁡(x))- (\sin{\left(x \right)} + \cos{\left(x \right)})
Simplify
The graph
Derivative of sin(x)-cos(x)
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