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^(3*x)
-
Derivative of x^3-3x^2
-
Derivative of x^2-x
-
Derivative of tan^-1(x)
-
Identical expressions
- (one /sqrt3)*arctg(sqrt(3x)/(one -x^ two))
- (1 divide by square root of 3) multiply by arctg( square root of (3x) divide by (1 minus x squared ))
- (one divide by square root of 3) multiply by arctg( square root of (3x) divide by (one minus x to the power of two))
- (1/√3)*arctg(√(3x)/(1-x^2))
- (1/sqrt3)*arctg(sqrt(3x)/(1-x2))
- 1/sqrt3*arctgsqrt3x/1-x2
- (1/sqrt3)*arctg(sqrt(3x)/(1-x²))
- (1/sqrt3)*arctg(sqrt(3x)/(1-x to the power of 2))
- (1/sqrt3)arctg(sqrt(3x)/(1-x^2))
- (1/sqrt3)arctg(sqrt(3x)/(1-x2))
- 1/sqrt3arctgsqrt3x/1-x2
- 1/sqrt3arctgsqrt3x/1-x^2
- (1 divide by sqrt3)*arctg(sqrt(3x) divide by (1-x^2))
-
Similar expressions
- (1/sqrt3)*arctg(sqrt(3x)/(1+x^2))
Derivative of (1/sqrt3)*arctg(sqrt(3x)/(1-x^2))
The solution
You have entered
[src]
/ _____\
|\/ 3*x |
atan|-------|
| 2|
\ 1 - x /
-------------
___
\/ 3
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{3 x}}{1 - x^{2}} \right)}}{\sqrt{3}}$$
atan(sqrt(3*x)/(1 - x^2))/sqrt(3)
The first derivative
[src]
___ / ___ ___ ___\
\/ 3 | \/ 3 2*x*\/ 3 *\/ x |
-----*|---------------- + ---------------|
3 | ___ / 2\ 2 |
|2*\/ x *\1 - x / / 2\ |
\ \1 - x / /
------------------------------------------
3*x
1 + ---------
2
/ 2\
\1 - x /
$$\frac{\frac{\sqrt{3}}{3} \left(\frac{2 x \sqrt{3} \sqrt{x}}{\left(1 - x^{2}\right)^{2}} + \frac{\sqrt{3}}{2 \sqrt{x} \left(1 - x^{2}\right)}\right)}{\frac{3 x}{\left(1 - x^{2}\right)^{2}} + 1}$$
The second derivative
[src]
/ 2 \ / 3/2\
| 4*x | | 1 4*x |
3*|-1 + -------|*|- ----- + -------|
5/2 ___ | 2| | ___ 2|
1 8*x 4*\/ x \ -1 + x / \ \/ x -1 + x /
------ - ---------- + ------- + ------------------------------------
3/2 2 2 2
4*x / 2\ -1 + x / 3*x \ / 2\
\-1 + x / 2*|1 + ----------|*\-1 + x /
| 2|
| / 2\ |
\ \-1 + x / /
--------------------------------------------------------------------
/ 3*x \ / 2\
|1 + ----------|*\-1 + x /
| 2|
| / 2\ |
\ \-1 + x / /
$$\frac{- \frac{8 x^{\frac{5}{2}}}{\left(x^{2} - 1\right)^{2}} + \frac{4 \sqrt{x}}{x^{2} - 1} + \frac{3 \left(\frac{4 x^{\frac{3}{2}}}{x^{2} - 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{2 \left(x^{2} - 1\right)^{2} \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + 1\right)} + \frac{1}{4 x^{\frac{3}{2}}}}{\left(x^{2} - 1\right) \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + 1\right)}$$
The third derivative
[src]
/ / 2 \ / 5/2 ___\ 2 \
| | 4*x | | 1 32*x 16*\/ x | / 2 \ / 3/2\ / 2 \ / 3/2\|
| |-1 + -------|*|---- - ---------- + --------| | 4*x | | 1 4*x | | 2*x | | 1 4*x ||
| | 2| | 3/2 2 2 | 3*|-1 + -------| *|- ----- + -------| 6*x*|-1 + -------|*|- ----- + -------||
| 3/2 7/2 \ -1 + x / |x / 2\ -1 + x | | 2| | ___ 2| | 2| | ___ 2||
| 1 1 12*x 16*x \ \-1 + x / / \ -1 + x / \ \/ x -1 + x / \ -1 + x / \ \/ x -1 + x /|
3*|- ------ + ----------------- - ---------- + ---------- + --------------------------------------------- + ------------------------------------- - --------------------------------------|
| 5/2 ___ / 2\ 2 3 2 2 4 3 |
| 8*x 2*\/ x *\-1 + x / / 2\ / 2\ / 3*x \ / 2\ / 3*x \ / 2\ / 3*x \ / 2\ |
| \-1 + x / \-1 + x / 2*|1 + ----------|*\-1 + x / |1 + ----------| *\-1 + x / |1 + ----------|*\-1 + x / |
| | 2| | 2| | 2| |
| | / 2\ | | / 2\ | | / 2\ | |
\ \ \-1 + x / / \ \-1 + x / / \ \-1 + x / / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 3*x \ / 2\
|1 + ----------|*\-1 + x /
| 2|
| / 2\ |
\ \-1 + x / /
$$\frac{3 \left(\frac{16 x^{\frac{7}{2}}}{\left(x^{2} - 1\right)^{3}} - \frac{12 x^{\frac{3}{2}}}{\left(x^{2} - 1\right)^{2}} - \frac{6 x \left(\frac{4 x^{\frac{3}{2}}}{x^{2} - 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{3} \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + 1\right)} + \frac{\left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \left(- \frac{32 x^{\frac{5}{2}}}{\left(x^{2} - 1\right)^{2}} + \frac{16 \sqrt{x}}{x^{2} - 1} + \frac{1}{x^{\frac{3}{2}}}\right)}{2 \left(x^{2} - 1\right)^{2} \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + 1\right)} + \frac{3 \left(\frac{4 x^{\frac{3}{2}}}{x^{2} - 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)^{2}}{\left(x^{2} - 1\right)^{4} \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + 1\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x^{2} - 1\right)} - \frac{1}{8 x^{\frac{5}{2}}}\right)}{\left(x^{2} - 1\right) \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + 1\right)}$$