Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of e^(2-x)
-
Derivative of x^(4/5)
-
Derivative of f(x)=5
-
Derivative of 2/x²
-
Identical expressions
- ln(x+ one /(x^ two + four)^(one / two))+ one / two arctg(x/2)
- ln(x plus 1 divide by (x squared plus 4) to the power of (1 divide by 2)) plus 1 divide by 2arctg(x divide by 2)
- ln(x plus one divide by (x to the power of two plus four) to the power of (one divide by two)) plus one divide by two arctg(x divide by 2)
- ln(x+1/(x2+4)(1/2))+1/2arctg(x/2)
- lnx+1/x2+41/2+1/2arctgx/2
- ln(x+1/(x²+4)^(1/2))+1/2arctg(x/2)
- ln(x+1/(x to the power of 2+4) to the power of (1/2))+1/2arctg(x/2)
- lnx+1/x^2+4^1/2+1/2arctgx/2
- ln(x+1 divide by (x^2+4)^(1 divide by 2))+1 divide by 2arctg(x divide by 2)
-
Similar expressions
- ln(x+1/(x^2-4)^(1/2))+1/2arctg(x/2)
- ln(x-1/(x^2+4)^(1/2))+1/2arctg(x/2)
- ln(x+1/(x^2+4)^(1/2))-1/2arctg(x/2)
Derivative of ln(x+1/(x^2+4)^(1/2))+1/2arctg(x/2)
The solution
You have entered
[src]
/x\
atan|-|
/ 1 \ \2/
log|x + -----------| + -------
| ________| 2
| / 2 |
\ \/ x + 4 /
$$\log{\left(x + \frac{1}{\sqrt{x^{2} + 4}} \right)} + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{2}$$
log(x + 1/(sqrt(x^2 + 4))) + atan(x/2)/2
The first derivative
[src]
x
1 - --------------------
________
/ 2 \ / 2
1 \x + 4/*\/ x + 4
---------- + ------------------------
/ 2\ 1
| x | x + -----------
4*|1 + --| ________
\ 4 / / 2
\/ x + 4
$$\frac{1}{4 \left(\frac{x^{2}}{4} + 1\right)} + \frac{- \frac{x}{\sqrt{x^{2} + 4} \left(x^{2} + 4\right)} + 1}{x + \frac{1}{\sqrt{x^{2} + 4}}}$$
The second derivative
[src]
2
/ x \ 2
|-1 + -----------| 3*x
| 3/2| -1 + ------
| / 2\ | 2
\ \4 + x / / 2*x 4 + x
- ------------------- - --------- + -----------------------------
2 2 3/2
/ 1 \ / 2\ / 2\ / 1 \
|x + -----------| \4 + x / \4 + x / *|x + -----------|
| ________| | ________|
| / 2 | | / 2 |
\ \/ 4 + x / \ \/ 4 + x /
$$- \frac{2 x}{\left(x^{2} + 4\right)^{2}} + \frac{\frac{3 x^{2}}{x^{2} + 4} - 1}{\left(x + \frac{1}{\sqrt{x^{2} + 4}}\right) \left(x^{2} + 4\right)^{\frac{3}{2}}} - \frac{\left(\frac{x}{\left(x^{2} + 4\right)^{\frac{3}{2}}} - 1\right)^{2}}{\left(x + \frac{1}{\sqrt{x^{2} + 4}}\right)^{2}}$$
The third derivative
[src]
3 / 2 \
/ x \ / 2 \ / x \ | 3*x |
2*|-1 + -----------| | 5*x | 3*|-1 + -----------|*|-1 + ------|
| 3/2| 3*x*|-3 + ------| | 3/2| | 2|
| / 2\ | 2 | 2| | / 2\ | \ 4 + x /
2 \ \4 + x / / 8*x \ 4 + x / \ \4 + x / /
- --------- - --------------------- + --------- - ----------------------------- + ----------------------------------
2 3 3 5/2 3/2 2
/ 2\ / 1 \ / 2\ / 2\ / 1 \ / 2\ / 1 \
\4 + x / |x + -----------| \4 + x / \4 + x / *|x + -----------| \4 + x / *|x + -----------|
| ________| | ________| | ________|
| / 2 | | / 2 | | / 2 |
\ \/ 4 + x / \ \/ 4 + x / \ \/ 4 + x /
$$\frac{8 x^{2}}{\left(x^{2} + 4\right)^{3}} - \frac{3 x \left(\frac{5 x^{2}}{x^{2} + 4} - 3\right)}{\left(x + \frac{1}{\sqrt{x^{2} + 4}}\right) \left(x^{2} + 4\right)^{\frac{5}{2}}} - \frac{2}{\left(x^{2} + 4\right)^{2}} + \frac{3 \left(\frac{x}{\left(x^{2} + 4\right)^{\frac{3}{2}}} - 1\right) \left(\frac{3 x^{2}}{x^{2} + 4} - 1\right)}{\left(x + \frac{1}{\sqrt{x^{2} + 4}}\right)^{2} \left(x^{2} + 4\right)^{\frac{3}{2}}} - \frac{2 \left(\frac{x}{\left(x^{2} + 4\right)^{\frac{3}{2}}} - 1\right)^{3}}{\left(x + \frac{1}{\sqrt{x^{2} + 4}}\right)^{3}}$$