Mister Exam

Derivative of sin(x)-cos(x)

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

The graph:

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Piecewise:

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)
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
The first derivative [src]
cos(x) + sin(x)
sin(x)+cos(x)\sin{\left(x \right)} + \cos{\left(x \right)}
The second derivative [src]
-sin(x) + cos(x)
sin(x)+cos(x)- \sin{\left(x \right)} + \cos{\left(x \right)}
The third derivative [src]
-(cos(x) + sin(x))
(sin(x)+cos(x))- (\sin{\left(x \right)} + \cos{\left(x \right)})
The graph
Derivative of sin(x)-cos(x)