Mister Exam

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The derivative of the function/ 2*cos(x)+x

Derivative of 2*cos(x)+x

The solution

You have entered [src]

2*cos(x) + x

$$x + 2 \cos{\left(x \right)}$$

2*cos(x) + x

Detail solution

Differentiate $x + 2 \cos{\left(x \right)}$ 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 cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $- 2 \sin{\left(x \right)}$
2. Apply the power rule: $x$ goes to $1$
The result is: $1 - 2 \sin{\left(x \right)}$

The answer is:

$1 - 2 \sin{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1 - 2*sin(x)

$$1 - 2 \sin{\left(x \right)}$$

Simplify

The second derivative [src]

-2*cos(x)

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

Simplify

The third derivative [src]

2*sin(x)

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

Simplify

The graph

Derivative of 2*cos(x)+x