Mister Exam

Lang:

The derivative of the function/ x-sin(x)

Derivative of x-sin(x)

The solution

You have entered [src]

x - sin(x)

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

x - sin(x)

Detail solution

Differentiate $x - \sin{\left(x \right)}$ term by term:
1. Apply the power rule: $x$ goes to $1$
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: $- \cos{\left(x \right)}$
The result is: $1 - \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1 - cos(x)

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

Simplify

The second derivative [src]

sin(x)

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

Simplify

The third derivative [src]

cos(x)

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

Simplify

The graph

Derivative of x-sin(x)