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The derivative of the function/ 6sinx-3x+0,5p+6

Derivative of 6sinx-3x+0,5p+6

The solution

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                 p    
6*sin(x) - 3*x + - + 6
                 2

$$\frac{p}{2} - 3 x + 6 \sin{\left(x \right)} + 6$$

d /                 p    \
--|6*sin(x) - 3*x + - + 6|
dx\                 2    /

$$\frac{\partial}{\partial x} \left(\frac{p}{2} - 3 x + 6 \sin{\left(x \right)} + 6\right)$$

Transform

Detail solution

Differentiate $\frac{p}{2} - 3 x + 6 \sin{\left(x \right)} + 6$ 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 sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $6 \cos{\left(x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $3$
  So, the result is: $-3$
3. The derivative of the constant $\frac{p}{2}$ is zero.
4. The derivative of the constant $6$ is zero.
The result is: $6 \cos{\left(x \right)} - 3$

The answer is:

$6 \cos{\left(x \right)} - 3$

The first derivative [src]

-3 + 6*cos(x)

$$6 \cos{\left(x \right)} - 3$$

Simplify

The second derivative [src]

-6*sin(x)

$$- 6 \sin{\left(x \right)}$$

Simplify

The third derivative [src]

-6*cos(x)

$$- 6 \cos{\left(x \right)}$$

Simplify