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3x^2-12*sqrt(x)

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Derivative of:
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Derivative of 5e^x
Derivative of 4-2x
Derivative of 3*(2-x)^6
Identical expressions
3x^ two - twelve *sqrt(x)
3x squared minus 12 multiply by square root of (x)
3x to the power of two minus twelve multiply by square root of (x)
3x^2-12*√(x)
3x2-12*sqrt(x)
3x2-12*sqrtx
3x²-12*sqrt(x)
3x to the power of 2-12*sqrt(x)
3x^2-12sqrt(x)
3x2-12sqrt(x)
3x2-12sqrtx
3x^2-12sqrtx
Similar expressions
3x^2+12*sqrt(x)

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

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

The solution

You have entered [src]

   2        ___
3*x  - 12*\/ x

$$3 x^{2} - 12 \sqrt{x}$$

d /   2        ___\
--\3*x  - 12*\/ x /
dx

$$\frac{d}{d x} \left(3 x^{2} - 12 \sqrt{x}\right)$$

Transform

Detail solution

Differentiate $- 12 \sqrt{x} + 3 x^{2}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $6 x$
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: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
    So, the result is: $\frac{6}{\sqrt{x}}$
  So, the result is: $- \frac{6}{\sqrt{x}}$
The result is: $6 x - \frac{6}{\sqrt{x}}$

The answer is:

$6 x - \frac{6}{\sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    6        
- ----- + 6*x
    ___      
  \/ x

$$6 x - \frac{6}{\sqrt{x}}$$

Simplify

The second derivative [src]

  /     1  \
3*|2 + ----|
  |     3/2|
  \    x   /

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

Simplify

The third derivative [src]

 -9   
------
   5/2
2*x

$$- \frac{9}{2 x^{\frac{5}{2}}}$$

Simplify

The graph

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