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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
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The graph:

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The solution

You have entered [src] 
x*sin(x)
xsin⁡(x)x \sin{\left(x \right)} 
x*sin(x)
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)=sin⁡(x)g{\left(x \right)} = \sin{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\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 is: xcos⁡(x)+sin⁡(x)x \cos{\left(x \right)} + \sin{\left(x \right)}

The answer is:

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