Mister Exam

Other calculators

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

Derivative of sin(x)-x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
sin(x) - x
$$- x + \sin{\left(x \right)}$$ 
d             
--(sin(x) - x)
dx
$$\frac{d}{d x} \left(- x + \sin{\left(x \right)}\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. The derivative of sine is cosine:

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-1 + cos(x)
$$\cos{\left(x \right)} - 1$$
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 sin(x)-x
    © Mister Exam – Calculator