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Derivative of:
Derivative of u
Derivative of e^x/x^2
Derivative of cos(x)/x^2
Derivative of cos(sqrt(x))
Integral of d{x}:
e^x/x^2
Limit of the function:
e^x/x^2
Graphing y =:
e^x/x^2
Identical expressions
e^x/x^ two
e to the power of x divide by x squared
e to the power of x divide by x to the power of two
ex/x2
e^x/x²
e to the power of x/x to the power of 2
e^x divide by x^2

The derivative of the function/ e^x/x^2

Derivative of e^x/x^2

The solution

You have entered [src]

 x
E 
--
 2
x

$$\frac{e^{x}}{x^{2}}$$

E^x/x^2

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = e^{x}$ and $g{\left(x \right)} = x^{2}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
Now plug in to the quotient rule:

$\frac{x^{2} e^{x} - 2 x e^{x}}{x^{4}}$
Now simplify:

$\frac{\left(x - 2\right) e^{x}}{x^{3}}$

The answer is:

$\frac{\left(x - 2\right) e^{x}}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x      x
e    2*e 
-- - ----
 2     3 
x     x

$$\frac{e^{x}}{x^{2}} - \frac{2 e^{x}}{x^{3}}$$

Simplify

The second derivative [src]

/    4   6 \  x
|1 - - + --|*e 
|    x    2|   
\        x /   
---------------
        2      
       x

$$\frac{\left(1 - \frac{4}{x} + \frac{6}{x^{2}}\right) e^{x}}{x^{2}}$$

Simplify

The third derivative [src]

/    24   6   18\  x
|1 - -- - - + --|*e 
|     3   x    2|   
\    x        x /   
--------------------
          2         
         x

$$\frac{\left(1 - \frac{6}{x} + \frac{18}{x^{2}} - \frac{24}{x^{3}}\right) e^{x}}{x^{2}}$$

Simplify

The graph

Derivative of e^x/x^2