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 (x^2+49)/x
-
Derivative of sec2x
-
Derivative of 6/x^4
-
Derivative of 2*x-x^2
-
Identical expressions
- arcsin((x/(x+ one)^(one / two)))
- arc sinus of ((x divide by (x plus 1) to the power of (1 divide by 2)))
- arc sinus of ((x divide by (x plus one) to the power of (one divide by two)))
- arcsin((x/(x+1)(1/2)))
- arcsinx/x+11/2
- arcsinx/x+1^1/2
- arcsin((x divide by (x+1)^(1 divide by 2)))
-
Similar expressions
- arcsin((x/(x-1)^(1/2)))
Derivative of arcsin((x/(x+1)^(1/2)))
The solution
You have entered
[src]
/ x \
asin|---------|
| _______|
\\/ x + 1 /
$$\operatorname{asin}{\left(\frac{x}{\sqrt{x + 1}} \right)}$$
asin(x/sqrt(x + 1))
The first derivative
[src]
1 x
--------- - ------------
_______ 3/2
\/ x + 1 2*(x + 1)
------------------------
___________
/ 2
/ x
/ 1 - -----
\/ x + 1
$$\frac{- \frac{x}{2 \left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x + 1}}}{\sqrt{- \frac{x^{2}}{x + 1} + 1}}$$
The second derivative
[src]
2
/ x \
x*|-2 + -----|
3*x \ 1 + x/
-1 + --------- + ---------------
4*(1 + x) / 2 \
| x |
4*|1 - -----|
\ 1 + x/
--------------------------------
___________
/ 2
3/2 / x
(1 + x) * / 1 - -----
\/ 1 + x
$$\frac{\frac{x \left(\frac{x}{x + 1} - 2\right)^{2}}{4 \left(- \frac{x^{2}}{x + 1} + 1\right)} + \frac{3 x}{4 \left(x + 1\right)} - 1}{\left(x + 1\right)^{\frac{3}{2}} \sqrt{- \frac{x^{2}}{x + 1} + 1}}$$
The third derivative
[src]
/ 2 \
/ x \ | x 2*x | 3
/ 5*x \ 4*|-2 + -----|*|1 + -------- - -----| 2 / x \ / x \ / 3*x \
3*|-6 + -----| \ 1 + x/ | 2 1 + x| 3*x *|-2 + -----| 2*x*|-2 + -----|*|4 - -----|
\ 1 + x/ \ (1 + x) / \ 1 + x/ \ 1 + x/ \ 1 + x/
- -------------- - ------------------------------------- - -------------------- + ----------------------------
1 + x 2 2 / 2 \
x / 2 \ | x |
1 - ----- | x | (1 + x)*|1 - -----|
1 + x (1 + x)*|1 - -----| \ 1 + x/
\ 1 + x/
--------------------------------------------------------------------------------------------------------------
___________
/ 2
3/2 / x
8*(1 + x) * / 1 - -----
\/ 1 + x
$$\frac{- \frac{3 x^{2} \left(\frac{x}{x + 1} - 2\right)^{3}}{\left(x + 1\right) \left(- \frac{x^{2}}{x + 1} + 1\right)^{2}} + \frac{2 x \left(- \frac{3 x}{x + 1} + 4\right) \left(\frac{x}{x + 1} - 2\right)}{\left(x + 1\right) \left(- \frac{x^{2}}{x + 1} + 1\right)} - \frac{4 \left(\frac{x}{x + 1} - 2\right) \left(\frac{x^{2}}{\left(x + 1\right)^{2}} - \frac{2 x}{x + 1} + 1\right)}{- \frac{x^{2}}{x + 1} + 1} - \frac{3 \left(\frac{5 x}{x + 1} - 6\right)}{x + 1}}{8 \left(x + 1\right)^{\frac{3}{2}} \sqrt{- \frac{x^{2}}{x + 1} + 1}}$$