Mister Exam

Lang:

The derivative of the function/ sinx/1-cosx

Derivative of sinx/1-cosx

The solution

You have entered [src]

sin(x)         
------ - cos(x)
  1

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

sin(x)/1 - cos(x)

Detail solution

Differentiate $\frac{\sin{\left(x \right)}}{1} - \cos{\left(x \right)}$ 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 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: $\sin{\left(x \right)}$
The result is: $\sin{\left(x \right)} + \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

cos(x) + sin(x)

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

Simplify

The second derivative [src]

-sin(x) + cos(x)

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of sinx/1-cosx