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x^2(x^3-sqrt(3)x)

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Derivative of:
Derivative of e^(-x)
Derivative of tanh(x)
Derivative of (x^2+1)^3
Derivative of cos(x)^(3)
Identical expressions
x^ two (x^ three -sqrt(three)x)
x squared (x cubed minus square root of (3)x)
x to the power of two (x to the power of three minus square root of (three)x)
x^2(x^3-√(3)x)
x2(x3-sqrt(3)x)
x2x3-sqrt3x
x²(x³-sqrt(3)x)
x to the power of 2(x to the power of 3-sqrt(3)x)
x^2x^3-sqrt3x
Similar expressions
x^2(x^3+sqrt(3)x)

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

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

The solution

You have entered [src]

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

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

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

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

Transform

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = x^{3} - \sqrt{3} x$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{3} - \sqrt{3} x$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  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: $x$ goes to $1$
      So, the result is: $\sqrt{3}$
    So, the result is: $- \sqrt{3}$
  The result is: $3 x^{2} - \sqrt{3}$
The result is: $x^{2} \cdot \left(3 x^{2} - \sqrt{3}\right) + 2 x \left(x^{3} - \sqrt{3} x\right)$
Now simplify:

$x^{2} \cdot \left(5 x^{2} - 3 \sqrt{3}\right)$

The answer is:

$x^{2} \cdot \left(5 x^{2} - 3 \sqrt{3}\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    /      ___       2\
2*x*\- 3*\/ 3  + 10*x /

$$2 x \left(10 x^{2} - 3 \sqrt{3}\right)$$

Simplify

The third derivative [src]

  /    ___       2\
6*\- \/ 3  + 10*x /

$$6 \cdot \left(10 x^{2} - \sqrt{3}\right)$$

Simplify

The graph

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