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Derivative of:
Derivative of x^-3
Derivative of x^2*sqrt(x)
Derivative of 1/2*x^2
Derivative of x*(log(x)/log(10))
Identical expressions
x^ six +x- one /x^ two
x to the power of 6 plus x minus 1 divide by x squared
x to the power of six plus x minus one divide by x to the power of two
x6+x-1/x2
x⁶+x-1/x²
x to the power of 6+x-1/x to the power of 2
x^6+x-1 divide by x^2
Similar expressions
x^6+x+1/x^2
x^6-x-1/x^2
What you mean?
(x^6 + x - 1*1)/(x^2)
(x^6 + x - 1*1)*2/x
(x^6 + x - 1*1)/(x^2)
x*(6 + x - 1*1)/(x^2)
x*(6 + x - 1*1)*2/x
x*(6 + x - 1*1)/(x^2)
x^6 + x - 1/(x^2)

The derivative of the function/ x^6+x-1/x^2

You entered:

x^6+x-1/x^2

What you mean?

(x^6 + x - 1*1)/(x^2)

(x^6 + x - 1*1)*2/x

(x^6 + x - 1*1)/(x^2)

x*(6 + x - 1*1)/(x^2)

x*(6 + x - 1*1)*2/x

x*(6 + x - 1*1)/(x^2)

x^6 + x - 1/(x^2)

Derivative of x^6+x-1/x^2

The solution

You have entered [src]

 6         1 
x  + x - 1*--
            2
           x

$$x^{6} + x - 1 \cdot \frac{1}{x^{2}}$$

d / 6         1 \
--|x  + x - 1*--|
dx|            2|
  \           x /

$$\frac{d}{d x} \left(x^{6} + x - 1 \cdot \frac{1}{x^{2}}\right)$$

Transform

Detail solution

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

The answer is:

$6 x^{5} + 1 + \frac{2}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2       5
1 + -- + 6*x 
     3       
    x

$$6 x^{5} + 1 + \frac{2}{x^{3}}$$

Simplify

The second derivative [src]

  /  1       4\
6*|- -- + 5*x |
  |   4       |
  \  x        /

$$6 \cdot \left(5 x^{4} - \frac{1}{x^{4}}\right)$$

Simplify

The third derivative [src]

   /1       3\
24*|-- + 5*x |
   | 5       |
   \x        /

$$24 \cdot \left(5 x^{3} + \frac{1}{x^{5}}\right)$$

Simplify

The graph

Derivative of x^6+x-1/x^2