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Identical expressions
(two sinx+3cosx)*x^2
(2 sinus of x plus 3 co sinus of e of x) multiply by x squared
(two sinus of x plus 3 co sinus of e of x) multiply by x squared
(2sinx+3cosx)*x2
2sinx+3cosx*x2
(2sinx+3cosx)*x²
(2sinx+3cosx)*x to the power of 2
(2sinx+3cosx)x^2
(2sinx+3cosx)x2
2sinx+3cosxx2
2sinx+3cosxx^2
Similar expressions
(2sinx-3cosx)*x^2

The derivative of the function/ (2sinx+3cosx)*x^2

Derivative of (2sinx+3cosx)*x^2

The solution

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                       2
(2*sin(x) + 3*cos(x))*x

$$x^{2} \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)$$

(2*sin(x) + 3*cos(x))*x^2

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = 2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$ term by term:
  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: $2 \cos{\left(x \right)}$
  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:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    So, the result is: $- 3 \sin{\left(x \right)}$
  The result is: $- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}$
$g{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
The result is: $x^{2} \left(- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 2 x \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)$
Now simplify:

$x \left(x \left(- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 4 \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right)$

The answer is:

$x \left(x \left(- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 4 \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2                                                   
x *(-3*sin(x) + 2*cos(x)) + 2*x*(2*sin(x) + 3*cos(x))

$$x^{2} \left(- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 2 x \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)$$

Simplify

The second derivative [src]

                       2                                                   
4*sin(x) + 6*cos(x) - x *(2*sin(x) + 3*cos(x)) - 4*x*(-2*cos(x) + 3*sin(x))

$$- x^{2} \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) - 4 x \left(3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) + 4 \sin{\left(x \right)} + 6 \cos{\left(x \right)}$$

Simplify

The third derivative [src]

                          2                                                   
-18*sin(x) + 12*cos(x) + x *(-2*cos(x) + 3*sin(x)) - 6*x*(2*sin(x) + 3*cos(x))

$$x^{2} \left(3 \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) - 6 x \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) - 18 \sin{\left(x \right)} + 12 \cos{\left(x \right)}$$

Simplify

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Derivative of (2sinx+3cosx)*x^2

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The solution