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sqrt(x)*(5*x-3)

How to use it?
Derivative of:
Derivative of (x+4)^1/2
Derivative of t-cos(t)
Derivative of tan(3)^(4)*x
Derivative of sqrt(x)^(4)
Graphing y =:
sqrt(x)*(5*x-3)
Identical expressions
sqrt(x)*(five *x- three)
square root of (x) multiply by (5 multiply by x minus 3)
square root of (x) multiply by (five multiply by x minus three)
√(x)*(5*x-3)
sqrt(x)(5x-3)
sqrtx5x-3
Similar expressions
sqrt(x)*(5*x+3)

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

Derivative of sqrt(x)(5x-3)

The solution

You have entered [src]

  ___          
\/ x *(5*x - 3)

$$\sqrt{x} \left(5 x - 3\right)$$

sqrt(x)*(5*x - 3)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = \sqrt{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
$g{\left(x \right)} = 5 x - 3$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $5 x - 3$ 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: $5$
  2. The derivative of the constant $-3$ is zero.
  The result is: $5$
The result is: $5 \sqrt{x} + \frac{5 x - 3}{2 \sqrt{x}}$
Now simplify:

$\frac{3 \left(5 x - 1\right)}{2 \sqrt{x}}$

The answer is:

$\frac{3 \left(5 x - 1\right)}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    -3 + 5*x
5 - --------
      4*x   
------------
     ___    
   \/ x

$$\frac{5 - \frac{5 x - 3}{4 x}}{\sqrt{x}}$$

Simplify

The third derivative [src]

  /      -3 + 5*x\
3*|-10 + --------|
  \         x    /
------------------
         3/2      
      8*x

$$\frac{3 \left(-10 + \frac{5 x - 3}{x}\right)}{8 x^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of sqrt(x)*(5*x-3)