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Derivative of:
Derivative of y=x^2sin(x)+2xcos(x)-2sin(x)
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Derivative of tg(2x)
Identical expressions
y=x^2sin(x)+2xcos(x)-2sin(x)
y equally x squared sinus of (x) plus 2x co sinus of e of (x) minus 2 sinus of (x)
y=x2sin(x)+2xcos(x)-2sin(x)
y=x2sinx+2xcosx-2sinx
y=x²sin(x)+2xcos(x)-2sin(x)
y=x to the power of 2sin(x)+2xcos(x)-2sin(x)
y=x^2sinx+2xcosx-2sinx
Similar expressions
x^2sinx+2xcosx-2sinx
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y=x^2sin(x)+2xcos(x)+2sin(x)
y=x^2sinx+2xcosx-2sinx
y=x^2sinx+2xcosx-2sinx

The derivative of the function/ y=x^2sin(x)+2xcos(x)-2sin(x)

Derivative of y=x^2sin(x)+2xcos(x)-2sin(x)

The solution

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 2                               
x *sin(x) + 2*x*cos(x) - 2*sin(x)

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

d / 2                               \
--\x *sin(x) + 2*x*cos(x) - 2*sin(x)/
dx

$$\frac{d}{d x} \left(x^{2} \sin{\left(x \right)} + 2 x \cos{\left(x \right)} - 2 \sin{\left(x \right)}\right)$$

Transform

Detail solution

Differentiate $x^{2} \sin{\left(x \right)} + 2 x \cos{\left(x \right)} - 2 \sin{\left(x \right)}$ term by term:
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  $g{\left(x \right)} = \sin{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  The result is: $x^{2} \cos{\left(x \right)} + 2 x \sin{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the product rule:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
    1. Apply the power rule: $x$ goes to $1$
    $g{\left(x \right)} = \cos{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
    1. The derivative of cosine is negative sine:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    The result is: $- x \sin{\left(x \right)} + \cos{\left(x \right)}$
  So, the result is: $- 2 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}$
3. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    So, the result is: $2 \cos{\left(x \right)}$
  So, the result is: $- 2 \cos{\left(x \right)}$
The result is: $x^{2} \cos{\left(x \right)}$

The answer is:

$x^{2} \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2       
x *cos(x)

$$x^{2} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

x*(2*cos(x) - x*sin(x))

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

Simplify

The third derivative [src]

            2                    
2*cos(x) - x *cos(x) - 4*x*sin(x)

$$- x^{2} \cos{\left(x \right)} - 4 x \sin{\left(x \right)} + 2 \cos{\left(x \right)}$$

Simplify

The graph

Derivative of y=x^2sin(x)+2xcos(x)-2sin(x)

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Identical expressions

Similar expressions

Derivative of y=x^2sin(x)+2xcos(x)-2sin(x)

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Piecewise:

The solution