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Derivative of:
Derivative of x/4
Derivative of e^3
Derivative of x^2*e^2*x
Derivative of 5^x^2
Integral of d{x}:
1/(x+3/4)
Identical expressions
one /(x+ three / four)
1 divide by (x plus 3 divide by 4)
one divide by (x plus three divide by four)
1/x+3/4
1 divide by (x+3 divide by 4)
Similar expressions
1/(x-3/4)

The derivative of the function/ 1/(x+3/4)

Derivative of 1/(x+3/4)

The solution

You have entered [src]

   1   
-------
x + 3/4

$$\frac{1}{x + \frac{3}{4}}$$

1/(x + 3/4)

Detail solution

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

$- \frac{1}{\left(x + \frac{3}{4}\right)^{2}}$
Now simplify:

$- \frac{16}{\left(4 x + 3\right)^{2}}$

The answer is:

$- \frac{16}{\left(4 x + 3\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -1     
----------
         2
(x + 3/4)

$$- \frac{1}{\left(x + \frac{3}{4}\right)^{2}}$$

Simplify

The second derivative [src]

    2     
----------
         3
(3/4 + x)

$$\frac{2}{\left(x + \frac{3}{4}\right)^{3}}$$

Simplify

The third derivative [src]

   -6     
----------
         4
(3/4 + x)

$$- \frac{6}{\left(x + \frac{3}{4}\right)^{4}}$$

Simplify