Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
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- Differential equations Step by Step
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How to use it?
- Derivative of:
- Derivative of x^x^x
-
Derivative of x^-11
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Derivative of (x+5)/(x+1)
- Derivative of -x/2
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Identical expressions
- asin(m*x/((two *d)))
- arc sinus of e of (m multiply by x divide by ((2 multiply by d)))
- arc sinus of e of (m multiply by x divide by ((two multiply by d)))
- asin(mx/((2d)))
- asinmx/2d
- asin(m*x divide by ((2*d)))
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Similar expressions
- arcsin(m*x/((2*d)))
Derivative of asin(m*x/((2*d)))
The solution
You have entered
[src]
/m*x\
asin|---|
\2*d/
$$\operatorname{asin}{\left(\frac{m x}{2 d} \right)}$$
asin((m*x)/((2*d)))
The first derivative
[src]
m
---------------------
___________
/ 2 2
/ m *x
2*d* / 1 - -----
/ 2
\/ 4*d
$$\frac{m}{2 d \sqrt{1 - \frac{m^{2} x^{2}}{4 d^{2}}}}$$
The second derivative
[src]
3
x*m
-------------------
3/2
/ 2 2\
3 | m *x |
8*d *|1 - -----|
| 2|
\ 4*d /
$$\frac{m^{3} x}{8 d^{3} \left(1 - \frac{m^{2} x^{2}}{4 d^{2}}\right)^{\frac{3}{2}}}$$
The third derivative
[src]
/ 2 2 \
3 | 3*m *x |
m *|4 + --------------|
| / 2 2\|
| 2 | m *x ||
| d *|1 - -----||
| | 2||
\ \ 4*d //
-----------------------
3/2
/ 2 2\
3 | m *x |
32*d *|1 - -----|
| 2|
\ 4*d /
$$\frac{m^{3} \left(4 + \frac{3 m^{2} x^{2}}{d^{2} \left(1 - \frac{m^{2} x^{2}}{4 d^{2}}\right)}\right)}{32 d^{3} \left(1 - \frac{m^{2} x^{2}}{4 d^{2}}\right)^{\frac{3}{2}}}$$