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Derivative of:
Derivative of x*e
Derivative of -cos(x)
Derivative of -4
Derivative of 2*sin(x)
Integral of d{x}:
cosx/1+2sinx
Equation:
cosx/1+2sinx
Identical expressions
cosx/ one +2sinx
co sinus of e of x divide by 1 plus 2 sinus of x
co sinus of e of x divide by one plus 2 sinus of x
cosx divide by 1+2sinx
Similar expressions
cosx/1-2sinx
cos(x)/(1+2*sin(x))
cos(x)/1+2*sin(x)

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

Derivative of cosx/1+2sinx

The solution

You have entered [src]

cos(x)           
------ + 2*sin(x)
  1

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

d /cos(x)           \
--|------ + 2*sin(x)|
dx\  1              /

$$\frac{d}{d x} \left(2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1}\right)$$

Transform

Detail solution

Differentiate $2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1}$ 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 cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $- \sin{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $2 \cos{\left(x \right)}$
The result is: $- \sin{\left(x \right)} + 2 \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

4-я производная [src]

2*sin(x) + cos(x)

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of cosx/1+2sinx