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Derivative of:
Derivative of (tgx+1)/(tgx-1)
Derivative of x^5-1/(15x^5)
Derivative of y=xarctgx
Derivative of e^(5-2x)
Identical expressions
x^ five - one /(1 five x^5)
x to the power of 5 minus 1 divide by (15x to the power of 5)
x to the power of five minus one divide by (1 five x to the power of 5)
x5-1/(15x5)
x5-1/15x5
x⁵-1/(15x⁵)
x^5-1/15x^5
x^5-1 divide by (15x^5)
Similar expressions
x^5+1/(15x^5)
What you mean?
(x^5 - 1*1)/((15*x^5))
(x^5 - 1*1)*5/(15*x)
(x^5 - 1*1)/((15*x)^5)
(x^5 - 1*1)*x^5/15
x*(5 - 1*1)/((15*x^5))
x*(5 - 1*1)*5/(15*x)
x^5 - x^5/15

The derivative of the function/ x^5-1/(15x^5)

You entered:

x^5-1/(15x^5)

What you mean?

(x^5 - 1*1)/((15*x^5))

(x^5 - 1*1)*5/(15*x)

(x^5 - 1*1)/((15*x)^5)

(x^5 - 1*1)*x^5/15

x*(5 - 1*1)/((15*x^5))

x*(5 - 1*1)*5/(15*x)

x^5 - x^5/15

Derivative of x^5-1/(15x^5)

The solution

You have entered [src]

 5       1  
x  - 1*-----
           5
       15*x

$$x^{5} - 1 \cdot \frac{1}{15 x^{5}}$$

d / 5       1  \
--|x  - 1*-----|
dx|           5|
  \       15*x /

$$\frac{d}{d x} \left(x^{5} - 1 \cdot \frac{1}{15 x^{5}}\right)$$

Transform

Detail solution

Differentiate $x^{5} - 1 \cdot \frac{1}{15 x^{5}}$ term by term:
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 15 x^{5}$ .
  2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 15 x^{5}$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
      So, the result is: $75 x^{4}$
    The result of the chain rule is:
    
    $- \frac{1}{3 x^{6}}$
  So, the result is: $\frac{1}{3 x^{6}}$
The result is: $5 x^{4} + \frac{1}{3 x^{6}}$
Now simplify:

$\frac{15 x^{10} + 1}{3 x^{6}}$

The answer is:

$\frac{15 x^{10} + 1}{3 x^{6}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   4    1  
5*x  + ----
          6
       3*x

$$5 x^{4} + \frac{1}{3 x^{6}}$$

Simplify

The second derivative [src]

  /  1        3\
2*|- -- + 10*x |
  |   7        |
  \  x         /

$$2 \cdot \left(10 x^{3} - \frac{1}{x^{7}}\right)$$

Simplify

The third derivative [src]

  /7        2\
2*|-- + 30*x |
  | 8        |
  \x         /

$$2 \cdot \left(30 x^{2} + \frac{7}{x^{8}}\right)$$

Simplify

The graph

Derivative of x^5-1/(15x^5)