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The derivative of the function/ x*cos(x)

Derivative of x*cos(x)

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

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from to

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The solution

You have entered [src] 
x*cos(x)
xcos⁡(x)x \cos{\left(x \right)} 
d           
--(x*cos(x))
dx
ddxxcos⁡(x)\frac{d}{d x} x \cos{\left(x \right)}
Transform
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=xf{\left(x \right)} = x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    g(x)=cos⁡(x)g{\left(x \right)} = \cos{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of cosine is negative sine:

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

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

The answer is:

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

The first derivative [src] 
-x*sin(x) + cos(x)
−xsin⁡(x)+cos⁡(x)- x \sin{\left(x \right)} + \cos{\left(x \right)}
Simplify
The second derivative [src] 
-(2*sin(x) + x*cos(x))
−(xcos⁡(x)+2sin⁡(x))- (x \cos{\left(x \right)} + 2 \sin{\left(x \right)})
Simplify
The third derivative [src] 
-3*cos(x) + x*sin(x)
xsin⁡(x)−3cos⁡(x)x \sin{\left(x \right)} - 3 \cos{\left(x \right)}
Simplify
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