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Derivative of:
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Identical expressions
y=sinx+ one /2cosx
y equally sinus of x plus 1 divide by 2 co sinus of e of x
y equally sinus of x plus one divide by 2 co sinus of e of x
y=sinx+1 divide by 2cosx
Similar expressions
y=sinx-1/2cosx

The derivative of the function/ y=sinx+1/2cosx

Derivative of y=sinx+1/2cosx

The solution

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

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

sin(x) + cos(x)/2

Detail solution

Differentiate $\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2}$ term by term:
1. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
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: $- \frac{\sin{\left(x \right)}}{2}$
The result is: $- \frac{\sin{\left(x \right)}}{2} + \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of y=sinx+1/2cosx