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Derivative of:
Derivative of sin(x)^2
Derivative of c
Derivative of x^4/log(x)
Derivative of log(x^2-6x+10)
Identical expressions
3sqrt(x)*(x+ four)
3 square root of (x) multiply by (x plus 4)
3 square root of (x) multiply by (x plus four)
3√(x)*(x+4)
3sqrt(x)(x+4)
3sqrtxx+4
Similar expressions
3sqrt(x)*(x-4)

The derivative of the function/ 3sqrt(x)*(x+4)

Derivative of 3sqrt(x)*(x+4)

The solution

You have entered [src]

    ___        
3*\/ x *(x + 4)

$$3 \sqrt{x} \left(x + 4\right)$$

(3*sqrt(x))*(x + 4)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = 3 \sqrt{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  So, the result is: $\frac{3}{2 \sqrt{x}}$
$g{\left(x \right)} = x + 4$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 4$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $4$ is zero.
  The result is: $1$
The result is: $3 \sqrt{x} + \frac{3 \left(x + 4\right)}{2 \sqrt{x}}$
Now simplify:

$\frac{3 \left(3 x + 4\right)}{2 \sqrt{x}}$

The answer is:

$\frac{3 \left(3 x + 4\right)}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    ___   3*(x + 4)
3*\/ x  + ---------
               ___ 
           2*\/ x

$$3 \sqrt{x} + \frac{3 \left(x + 4\right)}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

  /    4 + x\
3*|1 - -----|
  \     4*x /
-------------
      ___    
    \/ x

$$\frac{3 \left(1 - \frac{x + 4}{4 x}\right)}{\sqrt{x}}$$

Simplify

The third derivative [src]

  /     4 + x\
9*|-2 + -----|
  \       x  /
--------------
       3/2    
    8*x

$$\frac{9 \left(-2 + \frac{x + 4}{x}\right)}{8 x^{\frac{3}{2}}}$$

Simplify