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- Derivative of:
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Derivative of x^2*e^2
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Derivative of x^3+2*x^5
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Derivative of e^(x*(-4))
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Derivative of (x-6)x^3
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Identical expressions
- arcsin(sqrt(three)*x/sqrt(seven))
- arc sinus of ( square root of (3) multiply by x divide by square root of (7))
- arc sinus of ( square root of (three) multiply by x divide by square root of (seven))
- arcsin(√(3)*x/√(7))
- arcsin(sqrt(3)x/sqrt(7))
- arcsinsqrt3x/sqrt7
- arcsin(sqrt(3)*x divide by sqrt(7))
Derivative of arcsin(sqrt(3)*x/sqrt(7))
The solution
You have entered
[src]
/ ___ \
|\/ 3 *x|
asin|-------|
| ___ |
\ \/ 7 /
$$\operatorname{asin}{\left(\frac{\sqrt{3} x}{\sqrt{7}} \right)}$$
asin((sqrt(3)*x)/sqrt(7))
The first derivative
[src]
____
\/ 21
-----------------
__________
/ 2
/ 3*x
7* / 1 - ----
\/ 7
$$\frac{\sqrt{21}}{7 \sqrt{1 - \frac{3 x^{2}}{7}}}$$
The second derivative
[src]
____
3*x*\/ 21
----------------
3/2
/ 2\
| 3*x |
49*|1 - ----|
\ 7 /
$$\frac{3 \sqrt{21} x}{49 \left(1 - \frac{3 x^{2}}{7}\right)^{\frac{3}{2}}}$$
The third derivative
[src]
/ 2 \
____ | 9*x |
3*\/ 21 *|7 + --------|
| 2|
| 3*x |
| 1 - ----|
\ 7 /
-----------------------
3/2
/ 2\
| 3*x |
343*|1 - ----|
\ 7 /
$$\frac{3 \sqrt{21} \left(\frac{9 x^{2}}{1 - \frac{3 x^{2}}{7}} + 7\right)}{343 \left(1 - \frac{3 x^{2}}{7}\right)^{\frac{3}{2}}}$$