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5*sqrt(x)-7^5*(sqrt(x))^4+12^5*(sqrt(x))^3-5^6*(sqrt(x))^5

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  • Derivative of:
  • Derivative of 8^x Derivative of 8^x
  • Derivative of 2^x^2 Derivative of 2^x^2
  • Derivative of 1/(x+1)^2 Derivative of 1/(x+1)^2
  • Derivative of 1/(x+1) Derivative of 1/(x+1)

  • Identical expressions

  • five *sqrt(x)- seven ^ five *(sqrt(x))^ four + twelve ^ five *(sqrt(x))^ three - five ^ six *(sqrt(x))^ five
  • 5 multiply by square root of (x) minus 7 to the power of 5 multiply by ( square root of (x)) to the power of 4 plus 12 to the power of 5 multiply by ( square root of (x)) cubed minus 5 to the power of 6 multiply by ( square root of (x)) to the power of 5
  • five multiply by square root of (x) minus seven to the power of five multiply by ( square root of (x)) to the power of four plus twelve to the power of five multiply by ( square root of (x)) to the power of three minus five to the power of six multiply by ( square root of (x)) to the power of five
  • 5*√(x)-7^5*(√(x))^4+12^5*(√(x))^3-5^6*(√(x))^5
  • 5*sqrt(x)-75*(sqrt(x))4+125*(sqrt(x))3-56*(sqrt(x))5
  • 5*sqrtx-75*sqrtx4+125*sqrtx3-56*sqrtx5
  • 5*sqrt(x)-7⁵*(sqrt(x))⁴+12⁵*(sqrt(x))³-5⁶*(sqrt(x))⁵
  • 5*sqrt(x)-7 to the power of 5*(sqrt(x)) to the power of 4+12 to the power of 5*(sqrt(x)) to the power of 3-5 to the power of 6*(sqrt(x)) to the power of 5
  • 5sqrt(x)-7^5(sqrt(x))^4+12^5(sqrt(x))^3-5^6(sqrt(x))^5
  • 5sqrt(x)-75(sqrt(x))4+125(sqrt(x))3-56(sqrt(x))5
  • 5sqrtx-75sqrtx4+125sqrtx3-56sqrtx5
  • 5sqrtx-7^5sqrtx^4+12^5sqrtx^3-5^6sqrtx^5

  • Similar expressions

  • 5*sqrt(x)-7^5*(sqrt(x))^4-12^5*(sqrt(x))^3-5^6*(sqrt(x))^5
  • 5*sqrt(x)+7^5*(sqrt(x))^4+12^5*(sqrt(x))^3-5^6*(sqrt(x))^5
  • 5*sqrt(x)-7^5*(sqrt(x))^4+12^5*(sqrt(x))^3+5^6*(sqrt(x))^5
The derivative of the function/ 5*sqrt(x)-7^5*(sqrt(x))^4+12^5*(sqrt(x))^3-5^6*(sqrt(x))^5

Derivative of 5*sqrt(x)-7^5*(sqrt(x))^4+12^5*(sqrt(x))^3-5^6*(sqrt(x))^5

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                  4            3           5
    ___    5   ___      5   ___     6   ___ 
5*\/ x  - 7 *\/ x   + 12 *\/ x   - 5 *\/ x
$$- 5^{6} \left(\sqrt{x}\right)^{5} - 7^{5} \left(\sqrt{x}\right)^{4} + 12^{5} \left(\sqrt{x}\right)^{3} + 5 \sqrt{x}$$ 
  /                  4            3           5\
d |    ___    5   ___      5   ___     6   ___ |
--\5*\/ x  - 7 *\/ x   + 12 *\/ x   - 5 *\/ x  /
dx
$$\frac{d}{d x} \left(- 5^{6} \left(\sqrt{x}\right)^{5} - 7^{5} \left(\sqrt{x}\right)^{4} + 12^{5} \left(\sqrt{x}\right)^{3} + 5 \sqrt{x}\right)$$
Transform
Detail solution

  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. 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. Let .

        2. Apply the power rule: goes to

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

          1. Apply the power rule: goes to

          The result of the chain rule is:

        So, the result is:

      So, the result is:

    3. 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. Apply the power rule: goes to

        The result of the chain rule is:

      So, the result is:

    4. 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. Let .

        2. Apply the power rule: goes to

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

          1. Apply the power rule: goes to

          The result of the chain rule is:

        So, the result is:

      So, the result is:

    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] 
                                 3/2          
                    ___   78125*x         5   
-33614*x + 373248*\/ x  - ---------- + -------
                              2            ___
                                       2*\/ x
$$- \frac{78125 x^{\frac{3}{2}}}{2} + 373248 \sqrt{x} - 33614 x + \frac{5}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
                           ___         
         186624   234375*\/ x      5   
-33614 + ------ - ------------ - ------
           ___         4            3/2
         \/ x                    4*x
$$- \frac{234375 \sqrt{x}}{4} - 33614 + \frac{186624}{\sqrt{x}} - \frac{5}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  /  78125   31104    5  \
3*|- ----- - ----- + ----|
  |    8       x        2|
  \                  8*x /
--------------------------
            ___           
          \/ x
$$\frac{3 \left(- \frac{78125}{8} - \frac{31104}{x} + \frac{5}{8 x^{2}}\right)}{\sqrt{x}}$$
Simplify
The graph
Derivative of 5*sqrt(x)-7^5*(sqrt(x))^4+12^5*(sqrt(x))^3-5^6*(sqrt(x))^5
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