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 4/x^2
-
Derivative of cos(x^3)
-
Derivative of (cos(x))^3
-
Derivative of 1/tan(x)
-
Identical expressions
- z=y^arcsin((2y+ one)/ three)
- z equally y to the power of arc sinus of ((2y plus 1) divide by 3)
- z equally y to the power of arc sinus of ((2y plus one) divide by three)
- z=yarcsin((2y+1)/3)
- z=yarcsin2y+1/3
- z=y^arcsin2y+1/3
- z=y^arcsin((2y+1) divide by 3)
-
Similar expressions
- z=y^arcsin((2y-1)/3)
Derivative of z=y^arcsin((2y+1)/3)
The solution
You have entered
[src]
/2*y + 1\
asin|-------|
\ 3 /
y
$$y^{\operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}$$
y^asin((2*y + 1)/3)
Detail solution
-
Don't know the steps in finding this derivative.
But the derivative is
-
Now simplify:
The answer is:
The first derivative
[src]
/2*y + 1\ / /2*y + 1\ \
asin|-------| |asin|-------| |
\ 3 / | \ 3 / 2*log(y) |
y *|------------- + -----------------------|
| y ________________|
| / 2 |
| / (2*y + 1) |
| 3* / 1 - ---------- |
\ \/ 9 /
$$y^{\operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}} \left(\frac{2 \log{\left(y \right)}}{3 \sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} + \frac{\operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y}\right)$$
The second derivative
[src]
/ 2 \
|/ /1 + 2*y\\ |
|| 3*asin|-------|| |
|| 2*log(y) \ 3 /| |
||--------------------- + ---------------| |
|| ________________ y | |
|| / 2 | |
/1 + 2*y\ || / (1 + 2*y) | /1 + 2*y\ |
asin|-------| || / 1 - ---------- | asin|-------| |
\ 3 / |\\/ 9 / \ 3 / 4 4*(1 + 2*y)*log(y) |
y *|------------------------------------------ - ------------- + ------------------------- + ----------------------|
| 9 2 ________________ 3/2|
| y / 2 / 2\ |
| / (1 + 2*y) | (1 + 2*y) | |
| 3*y* / 1 - ---------- 27*|1 - ----------| |
\ \/ 9 \ 9 / /
$$y^{\operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}} \left(\frac{\left(\frac{2 \log{\left(y \right)}}{\sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} + \frac{3 \operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y}\right)^{2}}{9} + \frac{4 \left(2 y + 1\right) \log{\left(y \right)}}{27 \left(1 - \frac{\left(2 y + 1\right)^{2}}{9}\right)^{\frac{3}{2}}} + \frac{4}{3 y \sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} - \frac{\operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y^{2}}\right)$$
The third derivative
[src]
/ 3 \
|/ /1 + 2*y\\ / /1 + 2*y\\ / /1 + 2*y\ \ |
|| 3*asin|-------|| | 3*asin|-------|| | 27*asin|-------| | |
|| 2*log(y) \ 3 /| | 2*log(y) \ 3 /| | \ 3 / 36 4*(1 + 2*y)*log(y)| |
||--------------------- + ---------------| |--------------------- + ---------------|*|- ---------------- + ----------------------- + -------------------| |
|| ________________ y | | ________________ y | | 2 ________________ 3/2| |
|| / 2 | | / 2 | | y / 2 / 2\ | |
/1 + 2*y\ || / (1 + 2*y) | /1 + 2*y\ | / (1 + 2*y) | | / (1 + 2*y) | (1 + 2*y) | | |
asin|-------| || / 1 - ---------- | 2*asin|-------| | / 1 - ---------- | | y* / 1 - ---------- |1 - ----------| | 2 |
\ 3 / |\\/ 9 / 2 \ 3 / \\/ 9 / \ \/ 9 \ 9 / / 8*log(y) 4*(1 + 2*y) 8*(1 + 2*y) *log(y) |
y *|------------------------------------------ - ------------------------ + --------------- + -------------------------------------------------------------------------------------------------------------- + ---------------------- + ----------------------- + ----------------------|
| 27 ________________ 3 27 3/2 3/2 5/2|
| / 2 y / 2\ / 2\ / 2\ |
| 2 / (1 + 2*y) | (1 + 2*y) | | (1 + 2*y) | | (1 + 2*y) | |
| y * / 1 - ---------- 27*|1 - ----------| 9*y*|1 - ----------| 81*|1 - ----------| |
\ \/ 9 \ 9 / \ 9 / \ 9 / /
$$y^{\operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}} \left(\frac{\left(\frac{2 \log{\left(y \right)}}{\sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} + \frac{3 \operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y}\right)^{3}}{27} + \frac{\left(\frac{2 \log{\left(y \right)}}{\sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} + \frac{3 \operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y}\right) \left(\frac{4 \left(2 y + 1\right) \log{\left(y \right)}}{\left(1 - \frac{\left(2 y + 1\right)^{2}}{9}\right)^{\frac{3}{2}}} + \frac{36}{y \sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} - \frac{27 \operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y^{2}}\right)}{27} + \frac{8 \log{\left(y \right)}}{27 \left(1 - \frac{\left(2 y + 1\right)^{2}}{9}\right)^{\frac{3}{2}}} + \frac{8 \left(2 y + 1\right)^{2} \log{\left(y \right)}}{81 \left(1 - \frac{\left(2 y + 1\right)^{2}}{9}\right)^{\frac{5}{2}}} + \frac{4 \left(2 y + 1\right)}{9 y \left(1 - \frac{\left(2 y + 1\right)^{2}}{9}\right)^{\frac{3}{2}}} - \frac{2}{y^{2} \sqrt{1 - \frac{\left(2 y + 1\right)^{2}}{9}}} + \frac{2 \operatorname{asin}{\left(\frac{2 y + 1}{3} \right)}}{y^{3}}\right)$$
The graph