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- Derivative of:
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Derivative of x^-6
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Derivative of x^2*sqrt(1-x^2)
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Derivative of x^3*cot(x)
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Derivative of sin(x)+3
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Identical expressions
- asin((4x+ three)/(x^ two))
- arc sinus of e of ((4x plus 3) divide by (x squared ))
- arc sinus of e of ((4x plus three) divide by (x to the power of two))
- asin((4x+3)/(x2))
- asin4x+3/x2
- asin((4x+3)/(x²))
- asin((4x+3)/(x to the power of 2))
- asin4x+3/x^2
- asin((4x+3) divide by (x^2))
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Similar expressions
- asin((4x-3)/(x^2))
- arcsin((4x+3)/(x^2))
Derivative of asin((4x+3)/(x^2))
The solution
You have entered
[src]
/4*x + 3\
asin|-------|
| 2 |
\ x /
$$\operatorname{asin}{\left(\frac{4 x + 3}{x^{2}} \right)}$$
asin((4*x + 3)/x^2)
The first derivative
[src]
4 2*(4*x + 3)
-- - -----------
2 3
x x
----------------------
________________
/ 2
/ (4*x + 3)
/ 1 - ----------
/ 4
\/ x
$$\frac{\frac{4}{x^{2}} - \frac{2 \left(4 x + 3\right)}{x^{3}}}{\sqrt{1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}}}$$
The second derivative
[src]
/ 2 \
| / 3 + 4*x\ |
| 2*|2 - -------| *(3 + 4*x)|
| 3*(3 + 4*x) \ x / |
2*|-8 + ----------- + --------------------------|
| x / 2\ |
| 3 | (3 + 4*x) | |
| x *|1 - ----------| |
| | 4 | |
\ \ x / /
-------------------------------------------------
________________
/ 2
3 / (3 + 4*x)
x * / 1 - ----------
/ 4
\/ x
$$\frac{2 \left(-8 + \frac{3 \left(4 x + 3\right)}{x} + \frac{2 \left(2 - \frac{4 x + 3}{x}\right)^{2} \left(4 x + 3\right)}{x^{3} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)}\right)}{x^{3} \sqrt{1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}}}$$
The third derivative
[src]
/ / 2\ \
| / 3 + 4*x\ | 16*(3 + 4*x) 5*(3 + 4*x) | 3 |
| |2 - -------|*|8 - ------------ + ------------| / 3 + 4*x\ 2 / 3 + 4*x\ / 3*(3 + 4*x)\|
| \ x / | x 2 | 6*|2 - -------| *(3 + 4*x) 2*|2 - -------|*(3 + 4*x)*|8 - -----------||
| 6*(3 + 4*x) \ x / \ x / \ x / \ x /|
4*|18 - ----------- + ----------------------------------------------- + --------------------------- - -------------------------------------------|
| x / 2\ 2 / 2\ |
| 2 | (3 + 4*x) | / 2\ 3 | (3 + 4*x) | |
| x *|1 - ----------| 6 | (3 + 4*x) | x *|1 - ----------| |
| | 4 | x *|1 - ----------| | 4 | |
| \ x / | 4 | \ x / |
\ \ x / /
--------------------------------------------------------------------------------------------------------------------------------------------------
________________
/ 2
4 / (3 + 4*x)
x * / 1 - ----------
/ 4
\/ x
$$\frac{4 \left(18 - \frac{6 \left(4 x + 3\right)}{x} + \frac{\left(2 - \frac{4 x + 3}{x}\right) \left(8 - \frac{16 \left(4 x + 3\right)}{x} + \frac{5 \left(4 x + 3\right)^{2}}{x^{2}}\right)}{x^{2} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)} - \frac{2 \left(2 - \frac{4 x + 3}{x}\right) \left(8 - \frac{3 \left(4 x + 3\right)}{x}\right) \left(4 x + 3\right)}{x^{3} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)} + \frac{6 \left(2 - \frac{4 x + 3}{x}\right)^{3} \left(4 x + 3\right)^{2}}{x^{6} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)^{2}}\right)}{x^{4} \sqrt{1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}}}$$