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Derivative of:
Derivative of sin(x)^2
Derivative of x^-6
Derivative of ex^2
Derivative of e^sin(x)*cos(x)
Identical expressions
e*x*sin(x)/ two
e multiply by x multiply by sinus of (x) divide by 2
e multiply by x multiply by sinus of (x) divide by two
exsin(x)/2
exsinx/2
e*x*sin(x) divide by 2
Similar expressions
e*x*sinx/2

The derivative of the function/ e*x*sin(x)/2

Derivative of exsin(x)/2

The solution

You have entered [src]

E*x*sin(x)
----------
    2

$$\frac{e x \sin{\left(x \right)}}{2}$$

((E*x)*sin(x))/2

Detail solution

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. 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 $1$
    $g{\left(x \right)} = \sin{\left(x \right)}$ ; 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: $x \cos{\left(x \right)} + \sin{\left(x \right)}$
  So, the result is: $e \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)$
So, the result is: $\frac{e \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{2}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify