Mister Exam

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The derivative of the function/ sinx/1+sinx

Derivative of sinx/1+sinx

The solution

You have entered [src]

sin(x)         
------ + sin(x)
  1

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

sin(x)/1 + sin(x)

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*cos(x)

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

Simplify

The second derivative [src]

-2*sin(x)

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

Simplify

The third derivative [src]

-2*cos(x)

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

Simplify

The graph

Derivative of sinx/1+sinx