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5*(3*x+x^3-4*x^4)^3

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  • Derivative of:
  • Derivative of e^(1/x) Derivative of e^(1/x)
  • Derivative of x*x Derivative of x*x
  • Derivative of x^(3/4) Derivative of x^(3/4)
  • Derivative of (x-1)/(x+1) Derivative of (x-1)/(x+1)

  • Identical expressions

  • five *(three *x+x^ three - four *x^ four)^ three
  • 5 multiply by (3 multiply by x plus x cubed minus 4 multiply by x to the power of 4) cubed
  • five multiply by (three multiply by x plus x to the power of three minus four multiply by x to the power of four) to the power of three
  • 5*(3*x+x3-4*x4)3
  • 5*3*x+x3-4*x43
  • 5*(3*x+x³-4*x⁴)³
  • 5*(3*x+x to the power of 3-4*x to the power of 4) to the power of 3
  • 5(3x+x^3-4x^4)^3
  • 5(3x+x3-4x4)3
  • 53x+x3-4x43
  • 53x+x^3-4x^4^3

  • Similar expressions

  • 5*(3*x-x^3-4*x^4)^3
  • 5*(3*x+x^3+4*x^4)^3
The derivative of the function/ 5*(3*x+x^3-4*x^4)^3

Derivative of 5*(3*x+x^3-4*x^4)^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                   3
  /       3      4\ 
5*\3*x + x  - 4*x /
$$5 \left(- 4 x^{4} + x^{3} + 3 x\right)^{3}$$ 
  /                   3\
d |  /       3      4\ |
--\5*\3*x + x  - 4*x / /
dx
$$\frac{d}{d x} 5 \left(- 4 x^{4} + x^{3} + 3 x\right)^{3}$$
Transform
Detail solution

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

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate 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: goes to

          So, the result is:

        2. Apply the power rule: goes to

        3. 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: goes to

            So, the result is:

          So, the result is:

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                   2                   
  /       3      4\  /        3      2\
5*\3*x + x  - 4*x / *\9 - 48*x  + 9*x /
$$5 \left(- 48 x^{3} + 9 x^{2} + 9\right) \left(- 4 x^{4} + x^{3} + 3 x\right)^{2}$$
Simplify
The second derivative [src] 
      /                    2                                  \                
      |  /        3      2\       2            /     2      3\| /     2      3\
-30*x*\- \3 - 16*x  + 3*x /  + 3*x *(-1 + 8*x)*\3 + x  - 4*x //*\3 + x  - 4*x /
$$- 30 x \left(3 x^{2} \cdot \left(8 x - 1\right) \left(- 4 x^{3} + x^{2} + 3\right) - \left(- 16 x^{3} + 3 x^{2} + 3\right)^{2}\right) \left(- 4 x^{3} + x^{2} + 3\right)$$
Simplify
The third derivative [src] 
   /                  3                       2                                                                  \
   |/        3      2\       2 /     2      3\                    2            /     2      3\ /        3      2\|
30*\\3 - 16*x  + 3*x /  - 3*x *\3 + x  - 4*x / *(-1 + 16*x) - 18*x *(-1 + 8*x)*\3 + x  - 4*x /*\3 - 16*x  + 3*x //
$$30 \left(- 18 x^{2} \cdot \left(8 x - 1\right) \left(- 16 x^{3} + 3 x^{2} + 3\right) \left(- 4 x^{3} + x^{2} + 3\right) - 3 x^{2} \cdot \left(16 x - 1\right) \left(- 4 x^{3} + x^{2} + 3\right)^{2} + \left(- 16 x^{3} + 3 x^{2} + 3\right)^{3}\right)$$
Simplify
The graph
Derivative of 5*(3*x+x^3-4*x^4)^3
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