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3x^2-12*sqrt(x)
The derivative of the function/ 3x^2-12*sqrt(x)

Derivative of 3x^2-12*sqrt(x)

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
   2        ___
3*x  - 12*\/ x
3x2−12x3 x^{2} - 12 \sqrt{x} 
d /   2        ___\
--\3*x  - 12*\/ x /
dx
ddx(3x2−12x)\frac{d}{d x} \left(3 x^{2} - 12 \sqrt{x}\right)
Transform
Detail solution

  1. Differentiate −12x+3x2- 12 \sqrt{x} + 3 x^{2} 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: x2x^{2} goes to 2x2 x

      So, the result is: 6x6 x

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

        So, the result is: 6x\frac{6}{\sqrt{x}}

      So, the result is: −6x- \frac{6}{\sqrt{x}}

    The result is: 6x−6x6 x - \frac{6}{\sqrt{x}}

The answer is:

6x−6x6 x - \frac{6}{\sqrt{x}}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    6        
- ----- + 6*x
    ___      
  \/ x
6x−6x6 x - \frac{6}{\sqrt{x}}
Simplify
The second derivative [src] 
  /     1  \
3*|2 + ----|
  |     3/2|
  \    x   /
3⋅(2+1x32)3 \cdot \left(2 + \frac{1}{x^{\frac{3}{2}}}\right)
Simplify
The third derivative [src] 
 -9   
------
   5/2
2*x
−92x52- \frac{9}{2 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of 3x^2-12*sqrt(x)
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