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Derivative of:
Derivative of (4x-3)^2
Derivative of 8lnx
Derivative of (x+5)*sqrt(x)
Derivative of (x^2+1)^4
Identical expressions
- one / two sinx/2
minus 1 divide by 2 sinus of x divide by 2
minus one divide by two sinus of x divide by 2
-1 divide by 2sinx divide by 2
Similar expressions
1/2sinx/2

The derivative of the function/ -1/2sinx/2

Derivative of -1/2sinx/2

The solution

You have entered [src]

/-sin(x) \
|--------|
\   2    /
----------
    2

$$\frac{\left(-1\right) \frac{1}{2} \sin{\left(x \right)}}{2}$$

(-sin(x)/2)/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. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $- \frac{\cos{\left(x \right)}}{2}$
So, the result is: $- \frac{\cos{\left(x \right)}}{4}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-cos(x) 
--------
   4

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

Simplify

The second derivative [src]

sin(x)
------
  4

$$\frac{\sin{\left(x \right)}}{4}$$

Simplify

The third derivative [src]

cos(x)
------
  4

$$\frac{\cos{\left(x \right)}}{4}$$

Simplify