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Derivative of:
Derivative of sin(x)^2
Derivative of t-sint
Derivative of x^(3/2)-3*x+1
Derivative of x^2/(x^2+3)
Identical expressions
x^(three / two)- three *x+ one
x to the power of (3 divide by 2) minus 3 multiply by x plus 1
x to the power of (three divide by two) minus three multiply by x plus one
x(3/2)-3*x+1
x3/2-3*x+1
x^(3/2)-3x+1
x(3/2)-3x+1
x3/2-3x+1
x^3/2-3x+1
x^(3 divide by 2)-3*x+1
Similar expressions
x^(3/2)+3*x+1
x^(3/2)-3*x-1

The derivative of the function/ x^(3/2)-3*x+1

Derivative of x^(3/2)-3*x+1

The solution

You have entered [src]

 3/2          
x    - 3*x + 1

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

x^(3/2) - 3*x + 1

Detail solution

Differentiate $\left(x^{\frac{3}{2}} - 3 x\right) + 1$ term by term:
1. Differentiate $x^{\frac{3}{2}} - 3 x$ term by term:
  1. Apply the power rule: $x^{\frac{3}{2}}$ goes to $\frac{3 \sqrt{x}}{2}$
  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: $-3$
  The result is: $\frac{3 \sqrt{x}}{2} - 3$
2. The derivative of the constant $1$ is zero.
The result is: $\frac{3 \sqrt{x}}{2} - 3$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

 -3   
------
   3/2
8*x

$$- \frac{3}{8 x^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of x^(3/2)-3*x+1