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Derivative of:
Derivative of 5^(2*x)
Derivative of e^(sin(x)-2*x^3)
Derivative of 6*e^x
Derivative of 7/x^2
Identical expressions
(two *x- three)*sqrt(x)
(2 multiply by x minus 3) multiply by square root of (x)
(two multiply by x minus three) multiply by square root of (x)
(2*x-3)*√(x)
(2x-3)sqrt(x)
2x-3sqrtx
Similar expressions
sin^4*(2x-3sqrt(x))
(2*x+3)*sqrt(x)
(2x^2(x-3)sqrt(x-5))/(1-3x)^2

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

Derivative of (2x-3)sqrt(x)

The solution

You have entered [src]

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

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

(2*x - 3)*sqrt(x)

Detail solution

Apply the product rule:

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

$$\frac{2 - \frac{2 x - 3}{4 x}}{\sqrt{x}}$$

Simplify

The third derivative [src]

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

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

Simplify