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Derivative of:
Derivative of (x+2)
Derivative of 1+x
Derivative of 1/2*x
Derivative of e^x*cos(x)
Identical expressions
(- one)/(x+ four *x)
( minus 1) divide by (x plus 4 multiply by x)
( minus one) divide by (x plus four multiply by x)
(-1)/(x+4x)
-1/x+4x
(-1) divide by (x+4*x)
Similar expressions
(1)/(x+4*x)
(-1)/(x-4*x)

The derivative of the function/ (-1)/(x+4*x)

Derivative of (-1)/(x+4*x)

The solution

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  -1   
-------
x + 4*x

$$- \frac{1}{x + 4 x}$$

-1/(x + 4*x)

Detail solution

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

$\frac{1}{5 x^{2}}$

The answer is:

$\frac{1}{5 x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    5     
----------
         2
(x + 4*x)

$$\frac{5}{\left(x + 4 x\right)^{2}}$$

Simplify

The second derivative [src]

-2  
----
   3
5*x

$$- \frac{2}{5 x^{3}}$$

Simplify

The third derivative [src]

 6  
----
   4
5*x

$$\frac{6}{5 x^{4}}$$

Simplify