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Derivative of:
Derivative of (1-x^2)^(1/2)
Derivative of x-5
Derivative of 2*sinh(x)*cosh(x)
Derivative of x*ln(x)
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)= five /(seven *sqrtx^ seven (x^ five))
f(x) equally 5 divide by (7 multiply by square root of x to the power of 7(x to the power of 5))
f(x) equally five divide by (seven multiply by square root of x to the power of seven (x to the power of five))
f(x)=5/(7*√x^7(x^5))
f(x)=5/(7*sqrtx7(x5))
fx=5/7*sqrtx7x5
f(x)=5/(7*sqrtx⁷(x⁵))
f(x)=5/(7sqrtx^7(x^5))
f(x)=5/(7sqrtx7(x5))
fx=5/7sqrtx7x5
fx=5/7sqrtx^7x^5
f(x)=5 divide by (7*sqrtx^7(x^5))

The derivative of the function/ f(x)=5/(7*sqrtx^7(x^5))

Derivative of f(x)=5/(7*sqrtx^7(x^5))

The solution

You have entered [src]

     5     
-----------
       7   
    ___   5
7*\/ x  *x

$$\frac{5}{7 x^{5} \left(\sqrt{x}\right)^{7}}$$

d /     5     \
--|-----------|
dx|       7   |
  |    ___   5|
  \7*\/ x  *x /

$$\frac{d}{d x} \frac{5}{7 x^{5} \left(\sqrt{x}\right)^{7}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 7 x^{5} \left(\sqrt{x}\right)^{7}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 7 x^{5} \left(\sqrt{x}\right)^{7}$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the product rule:
      
      $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
      
      $f{\left(x \right)} = x^{5}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
      1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
      $g{\left(x \right)} = \left(\sqrt{x}\right)^{7}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
      1. Let $u = \sqrt{x}$ .
      2. Apply the power rule: $u^{7}$ goes to $7 u^{6}$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
        
        Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
        
        The result of the chain rule is:
        
        $\frac{7 x^{\frac{5}{2}}}{2}$
      The result is: $\frac{7 x^{\frac{15}{2}}}{2} + 5 x^{\frac{7}{2}} x^{4}$
    So, the result is: $\frac{49 x^{\frac{15}{2}}}{2} + 35 x^{\frac{7}{2}} x^{4}$
  The result of the chain rule is:
  
  $- \frac{\frac{49 x^{\frac{15}{2}}}{2} + 35 x^{\frac{7}{2}} x^{4}}{49 x^{17}}$
So, the result is: $- \frac{5 \cdot \left(\frac{49 x^{\frac{15}{2}}}{2} + 35 x^{\frac{7}{2}} x^{4}\right)}{49 x^{17}}$
Now simplify:

$- \frac{85}{14 x^{\frac{19}{2}}}$

The answer is:

$- \frac{85}{14 x^{\frac{19}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  /      15/2             \
  |  49*x           4  7/2|
5*|- -------- - 35*x *x   |
  \     2                 /
---------------------------
               17          
           49*x

$$\frac{5 \left(- \frac{49 x^{\frac{15}{2}}}{2} - 35 x^{\frac{7}{2}} x^{4}\right)}{49 x^{17}}$$

Simplify

The second derivative [src]

  1615  
--------
    21/2
28*x

$$\frac{1615}{28 x^{\frac{21}{2}}}$$

Simplify

The third derivative [src]

 -4845 
-------
   23/2
8*x

$$- \frac{4845}{8 x^{\frac{23}{2}}}$$

Simplify

The graph

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Identical expressions

Derivative of f(x)=5/(7*sqrtx^7(x^5))

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The solution