Mister Exam

Lang:

The derivative of the function/ 6\root(3)(x)-4\root(4)(x)

Derivative of 6\root(3)(x)-4\root(4)(x)

The solution

You have entered [src]

  6         4    
-----*x - -----*x
  ___       ___  
\/ 3      \/ 4

$$- x \frac{4}{\sqrt{4}} + x \frac{6}{\sqrt{3}}$$

(6/sqrt(3))*x - 4/sqrt(4)*x

Detail solution

Differentiate $- x \frac{4}{\sqrt{4}} + x \frac{6}{\sqrt{3}}$ 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: $\frac{6}{\sqrt{3}}$
2. 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: $-2$
The result is: $-2 + \frac{6}{\sqrt{3}}$
Now simplify:

$-2 + 2 \sqrt{3}$

The answer is:

$-2 + 2 \sqrt{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       6  
-2 + -----
       ___
     \/ 3

$$-2 + \frac{6}{\sqrt{3}}$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify