Mister Exam

Derivative of 2*x*cos(x)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
2*x*cos(x)
2xcos(x)2 x \cos{\left(x \right)}
(2*x)*cos(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)=2xf{\left(x \right)} = 2 x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

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

      1. Apply the power rule: xx goes to 11

      So, the result is: 22

    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: 2xsin(x)+2cos(x)- 2 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}


The answer is:

2xsin(x)+2cos(x)- 2 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}

The graph
02468-8-6-4-2-1010-5050
The first derivative [src]
2*cos(x) - 2*x*sin(x)
2xsin(x)+2cos(x)- 2 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}
The second derivative [src]
-2*(2*sin(x) + x*cos(x))
2(xcos(x)+2sin(x))- 2 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)
The third derivative [src]
2*(-3*cos(x) + x*sin(x))
2(xsin(x)3cos(x))2 \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)
The graph
Derivative of 2*x*cos(x)