Mister Exam

Lang:

Derivative of atan(2)/(x-3)

You have entered [src]

atan(2)
-------
 x - 3

$$\frac{\operatorname{atan}{\left(2 \right)}}{x - 3}$$

d /atan(2)\
--|-------|
dx\ x - 3 /

$$\frac{d}{d x} \frac{\operatorname{atan}{\left(2 \right)}}{x - 3}$$

Transform

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-atan(2) 
---------
        2
 (x - 3)

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

Simplify

The second derivative [src]

2*atan(2)
---------
        3
(-3 + x)

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

Simplify

The third derivative [src]

-6*atan(2)
----------
        4 
(-3 + x)

$$- \frac{6 \operatorname{atan}{\left(2 \right)}}{\left(x - 3\right)^{4}}$$

Simplify

The graph