Mister Exam

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The derivative of the function/ 3x-1/2x+1

Derivative of 3x-1/2x+1

The solution

You have entered [src]

      x    
3*x - - + 1
      2

$$- \frac{x}{2} + 3 x + 1$$

d /      x    \
--|3*x - - + 1|
dx\      2    /

$$\frac{d}{d x} \left(- \frac{x}{2} + 3 x + 1\right)$$

Transform

Detail solution

Differentiate $- \frac{x}{2} + 3 x + 1$ term by term:
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: $3$
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: $\frac{1}{2}$
  So, the result is: $- \frac{1}{2}$
3. The derivative of the constant $1$ is zero.
The result is: $\frac{5}{2}$

The answer is:

$\frac{5}{2}$

The first derivative [src]

5/2

$$\frac{5}{2}$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify