Mister Exam

Other calculators

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

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 3/2          
x    - 3*x + 1
(x32−3x)+1\left(x^{\frac{3}{2}} - 3 x\right) + 1 
x^(3/2) - 3*x + 1
Detail solution

  1. Differentiate (x32−3x)+1\left(x^{\frac{3}{2}} - 3 x\right) + 1 term by term:

    1. Differentiate x32−3xx^{\frac{3}{2}} - 3 x term by term:

      1. Apply the power rule: x32x^{\frac{3}{2}} goes to 3x2\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: xx goes to 11

        So, the result is: −3-3

      The result is: 3x2−3\frac{3 \sqrt{x}}{2} - 3

    2. The derivative of the constant 11 is zero.

    The result is: 3x2−3\frac{3 \sqrt{x}}{2} - 3

The answer is:

3x2−3\frac{3 \sqrt{x}}{2} - 3

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
         ___
     3*\/ x 
-3 + -------
        2
3x2−3\frac{3 \sqrt{x}}{2} - 3
Simplify
The second derivative [src] 
   3   
-------
    ___
4*\/ x
34x\frac{3}{4 \sqrt{x}}
Simplify
The third derivative [src] 
 -3   
------
   3/2
8*x
−38x32- \frac{3}{8 x^{\frac{3}{2}}}
Simplify
The graph
Derivative of x^(3/2)-3*x+1
    © Mister Exam – Calculator