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$y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))$

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Derivative of:
Derivative of sqrt(x-2)
$Derivative of y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))$ Derivative of y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))
Derivative of csc7x
Derivative of sin(pix/2)
Identical expressions
y=(\root(seven)(x^(four))- four \root(three)(x^(two))+(one)/(two))/(\root(five)(x^(three)))
y equally (\root(7)(x to the power of (4)) minus 4\root(3)(x to the power of (2)) plus (1) divide by (2)) divide by (\root(5)(x to the power of (3)))
y equally (\root(seven)(x to the power of (four)) minus four \root(three)(x to the power of (two)) plus (one) divide by (two)) divide by (\root(five)(x to the power of (three)))
y=(\root(7)(x(4))-4\root(3)(x(2))+(1)/(2))/(\root(5)(x(3)))
y=\root7x4-4\root3x2+1/2/\root5x3
y=\root7x^4-4\root3x^2+1/2/\root5x^3
y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1) divide by (2)) divide by (\root(5)(x^(3)))
Similar expressions
y=(\root(7)(x^(4))+4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))
y=(\root(7)(x^(4))-4\root(3)(x^(2))-(1)/(2))/(\root(5)(x^(3)))

The derivative of the function/ y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))

Derivative of y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))

The solution

You have entered [src]

  ___  4     4    2      
\/ 7 *x  - -----*x  + 0.5
             ___         
           \/ 3          
-------------------------
           ___  3        
         \/ 5 *x

$$\frac{\left(\sqrt{7} x^{4} - x^{2} \frac{4}{\sqrt{3}}\right) + 0.5}{\sqrt{5} x^{3}}$$

(sqrt(7)*x^4 - 4/sqrt(3)*x^2 + 0.5)/((sqrt(5)*x^3))

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = \sqrt{21} x^{4} - 4 x^{2} + 0.5 \sqrt{3}$ and $g{\left(x \right)} = \sqrt{15} x^{3}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $\sqrt{21} x^{4} - 4 x^{2} + 0.5 \sqrt{3}$ 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: $- 8 x$
  2. The derivative of the constant $0.5 \sqrt{3}$ is zero.
  3. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
    So, the result is: $4 \sqrt{21} x^{3}$
  The result is: $4 \sqrt{21} x^{3} - 8 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $3 \sqrt{15} x^{2}$
Now plug in to the quotient rule:

$\frac{\sqrt{15} x^{3} \left(4 \sqrt{21} x^{3} - 8 x\right) - 3 \sqrt{15} x^{2} \left(\sqrt{21} x^{4} - 4 x^{2} + 0.5 \sqrt{3}\right)}{15 x^{6}}$
Now simplify:

$0.2 \sqrt{35} + \frac{0.266666666666667 \sqrt{15}}{x^{2}} - \frac{0.3 \sqrt{5}}{x^{4}}$

The answer is:

$0.2 \sqrt{35} + \frac{0.266666666666667 \sqrt{15}}{x^{2}} - \frac{0.3 \sqrt{5}}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                                     ___ /  ___  4     4    2      \
                                 3*\/ 5 *|\/ 7 *x  - -----*x  + 0.5|
  ___ /                   ___\           |             ___         |
\/ 5  |    ___  3   8*x*\/ 3 |           \           \/ 3          /
-----*|4*\/ 7 *x  - ---------| - -----------------------------------
    3 \                 3    /                      4               
 5*x                                             5*x

$$\frac{\sqrt{5}}{5 x^{3}} \left(4 \sqrt{7} x^{3} - \frac{8 \sqrt{3} x}{3}\right) - \frac{3 \sqrt{5} \left(\left(\sqrt{7} x^{4} - x^{2} \frac{4}{\sqrt{3}}\right) + 0.5\right)}{5 x^{4}}$$

Simplify

The second derivative [src]

        /     ___             ___  2       ___  4             \
    ___ |10*\/ 3    1.5 - 4*\/ 3 *x  + 3*\/ 7 *x        ___  2|
4*\/ 5 *|-------- + ----------------------------- - 3*\/ 7 *x |
        |   3                      2                          |
        \                         x                           /
---------------------------------------------------------------
                                 3                             
                              5*x

$$\frac{4 \sqrt{5} \left(- 3 \sqrt{7} x^{2} + \frac{10 \sqrt{3}}{3} + \frac{3 \sqrt{7} x^{4} - 4 \sqrt{3} x^{2} + 1.5}{x^{2}}\right)}{5 x^{3}}$$

Simplify

The third derivative [src]

  /               ___ /          ___  2       ___  4\       ___ /      ___       ___  2\        ___ /      ___       ___  2\\
  |    ____   5*\/ 5 *\1.5 - 4*\/ 3 *x  + 3*\/ 7 *x /   3*\/ 5 *\- 2*\/ 3  + 9*\/ 7 *x /   12*\/ 5 *\- 2*\/ 3  + 3*\/ 7 *x /|
4*|6*\/ 35  - --------------------------------------- - -------------------------------- + ---------------------------------|
  |                               4                                     2                                   2               |
  \                              x                                     x                                   x                /
-----------------------------------------------------------------------------------------------------------------------------
                                                                2                                                            
                                                             5*x

$$\frac{4 \left(6 \sqrt{35} + \frac{12 \sqrt{5} \left(3 \sqrt{7} x^{2} - 2 \sqrt{3}\right)}{x^{2}} - \frac{3 \sqrt{5} \left(9 \sqrt{7} x^{2} - 2 \sqrt{3}\right)}{x^{2}} - \frac{5 \sqrt{5} \left(3 \sqrt{7} x^{4} - 4 \sqrt{3} x^{2} + 1.5\right)}{x^{4}}\right)}{5 x^{2}}$$

Simplify

The graph

$Derivative of y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))$

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of y=(\root(7)(x^(4))-4\root(3)(x^(2))+(1)/(2))/(\root(5)(x^(3)))

The graph:

Piecewise:

The solution