Mister Exam

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The derivative of the function/ 4(1-cos(x))

Derivative of 4(1-cos(x))

The solution

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4*(1 - cos(x))

$$4 \left(1 - \cos{\left(x \right)}\right)$$

4*(1 - cos(x))

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $1 - \cos{\left(x \right)}$ term by term:
  1. The derivative of the constant $1$ is zero.
  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: $\sin{\left(x \right)}$
So, the result is: $4 \sin{\left(x \right)}$

The answer is:

$4 \sin{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4*sin(x)

$$4 \sin{\left(x \right)}$$

Simplify

The second derivative [src]

4*cos(x)

$$4 \cos{\left(x \right)}$$

Simplify

The third derivative [src]

-4*sin(x)

$$- 4 \sin{\left(x \right)}$$

Simplify