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Derivative of:
Derivative of c
Derivative of log(x^2-6x+10)
Derivative of ln((x+a)^0.5)
Derivative of f(x)=sec(x)
Identical expressions
one /x^ seven +lnx
1 divide by x to the power of 7 plus lnx
one divide by x to the power of seven plus lnx
1/x7+lnx
1/x⁷+lnx
1 divide by x^7+lnx
Similar expressions
1/x^7-lnx

The derivative of the function/ 1/x^7+lnx

Derivative of 1/x^7+lnx

The solution

You have entered [src]

1          
-- + log(x)
 7         
x

$$\log{\left(x \right)} + \frac{1}{x^{7}}$$

1/(x^7) + log(x)

Detail solution

Differentiate $\log{\left(x \right)} + \frac{1}{x^{7}}$ term by term:
1. Let $u = x^{7}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{7}$ :
  1. Apply the power rule: $x^{7}$ goes to $7 x^{6}$
  The result of the chain rule is:
  
  $- \frac{7}{x^{8}}$
4. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
The result is: $\frac{1}{x} - \frac{7}{x^{8}}$
Now simplify:

$\frac{x^{7} - 7}{x^{8}}$

The answer is:

$\frac{x^{7} - 7}{x^{8}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1    7  
- - ----
x      7
    x*x

$$\frac{1}{x} - \frac{7}{x x^{7}}$$

Simplify

The second derivative [src]

     56
-1 + --
      7
     x 
-------
    2  
   x

$$\frac{-1 + \frac{56}{x^{7}}}{x^{2}}$$

Simplify

The third derivative [src]

  /    252\
2*|1 - ---|
  |      7|
  \     x /
-----------
      3    
     x

$$\frac{2 \left(1 - \frac{252}{x^{7}}\right)}{x^{3}}$$

Simplify