Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 4/x^2
Derivative of cos(x^3)
Derivative of (cos(x))^3
Derivative of 1/tan(x)
Identical expressions
five *sqrt(three *x+ two)/ three
5 multiply by square root of (3 multiply by x plus 2) divide by 3
five multiply by square root of (three multiply by x plus two) divide by three
5*√(3*x+2)/3
5sqrt(3x+2)/3
5sqrt3x+2/3
5*sqrt(3*x+2) divide by 3
Similar expressions
5*sqrt(3*x-2)/3

The derivative of the function/ 5*sqrt(3*x+2)/3

Derivative of 5sqrt(3x+2)/3

The solution

You have entered [src]

    _________
5*\/ 3*x + 2 
-------------
      3

$$\frac{5 \sqrt{3 x + 2}}{3}$$

(5*sqrt(3*x + 2))/3

Detail solution

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. Let $u = 3 x + 2$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 2\right)$ :
    1. Differentiate $3 x + 2$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $3$
      2. The derivative of the constant $2$ is zero.
      The result is: $3$
    The result of the chain rule is:
    
    $\frac{3}{2 \sqrt{3 x + 2}}$
  So, the result is: $\frac{15}{2 \sqrt{3 x + 2}}$
So, the result is: $\frac{5}{2 \sqrt{3 x + 2}}$
Now simplify:

$\frac{5}{2 \sqrt{3 x + 2}}$

The answer is:

$\frac{5}{2 \sqrt{3 x + 2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      5      
-------------
    _________
2*\/ 3*x + 2

$$\frac{5}{2 \sqrt{3 x + 2}}$$

Simplify

The second derivative [src]

     -15      
--------------
           3/2
4*(2 + 3*x)

$$- \frac{15}{4 \left(3 x + 2\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

     135      
--------------
           5/2
8*(2 + 3*x)

$$\frac{135}{8 \left(3 x + 2\right)^{\frac{5}{2}}}$$

Simplify