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Derivative of:
Derivative of x^cosx
Derivative of y=9
Derivative of y=7x+4
Derivative of -x^3+4*x^2-4*x
Identical expressions
c/ two sinx^2
c divide by 2 sinus of x squared
c divide by two sinus of x squared
c/2sinx2
c/2sinx²
c/2sinx to the power of 2
c divide by 2sinx^2

The derivative of the function/ c/2sinx^2

Derivative of c/2sinx^2

The solution

You have entered [src]

     2   
c*sin (x)
---------
    2

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

  /     2   \
d |c*sin (x)|
--|---------|
dx\    2    /

$$\frac{\partial}{\partial x} \frac{c \sin^{2}{\left(x \right)}}{2}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sin{\left(x \right)}$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  The result of the chain rule is:
  
  $2 \sin{\left(x \right)} \cos{\left(x \right)}$
So, the result is: $c \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

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

The answer is:

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

The first derivative [src]

c*cos(x)*sin(x)

$$c \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

   /   2         2   \
-c*\sin (x) - cos (x)/

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

Simplify

The third derivative [src]

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

$$- 4 c \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify