Mister Exam

Lang:

The derivative of the function/ 2*(t-sin(t))

Derivative of 2*(t-sin(t))

The solution

You have entered [src]

2*(t - sin(t))

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

d                 
--(2*(t - sin(t)))
dt

$$\frac{d}{d t} 2 \left(t - \sin{\left(t \right)}\right)$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $t - \sin{\left(t \right)}$ term by term:
  1. Apply the power rule: $t$ 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:
      
      $\frac{d}{d t} \sin{\left(t \right)} = \cos{\left(t \right)}$
    So, the result is: $- \cos{\left(t \right)}$
  The result is: $1 - \cos{\left(t \right)}$
So, the result is: $2 - 2 \cos{\left(t \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2 - 2*cos(t)

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

Simplify

The second derivative [src]

2*sin(t)

$$2 \sin{\left(t \right)}$$

Simplify

The third derivative [src]

2*cos(t)

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

Simplify

The graph

Derivative of 2*(t-sin(t))