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How to use it?
- Derivative of:
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Derivative of x^12
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Derivative of x^2*e^(3-2*x)*log(2)^x
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Derivative of -(x^2+324)/x
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Derivative of x^3-1/5*x^2+2*x-4
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Identical expressions
- asin(x/ three)*sin(two *x)
- arc sinus of e of (x divide by 3) multiply by sinus of (2 multiply by x)
- arc sinus of e of (x divide by three) multiply by sinus of (two multiply by x)
- asin(x/3)sin(2x)
- asinx/3sin2x
- asin(x divide by 3)*sin(2*x)
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Similar expressions
- arcsin(x/3)*sin(2*x)
Derivative of asin(x/3)*sin(2*x)
The solution
You have entered
[src]
/x\
asin|-|*sin(2*x)
\3/
$$\sin{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)}$$
asin(x/3)*sin(2*x)
The first derivative
[src]
/x\ sin(2*x)
2*asin|-|*cos(2*x) + ---------------
\3/ ________
/ 2
/ x
3* / 1 - --
\/ 9
$$2 \cos{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} + \frac{\sin{\left(2 x \right)}}{3 \sqrt{1 - \frac{x^{2}}{9}}}$$
The second derivative
[src]
/x\ 4*cos(2*x) x*sin(2*x)
- 4*asin|-|*sin(2*x) + --------------- + --------------
\3/ ________ 3/2
/ 2 / 2\
/ x | x |
3* / 1 - -- 27*|1 - --|
\/ 9 \ 9 /
$$\frac{x \sin{\left(2 x \right)}}{27 \left(1 - \frac{x^{2}}{9}\right)^{\frac{3}{2}}} - 4 \sin{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} + \frac{4 \cos{\left(2 x \right)}}{3 \sqrt{1 - \frac{x^{2}}{9}}}$$
The third derivative
[src]
/ 2 \
| 3*x |
|-1 + -------|*sin(2*x)
| 2|
/x\ 4*sin(2*x) \ -9 + x / 2*x*cos(2*x)
- 8*asin|-|*cos(2*x) - ------------- - ----------------------- + -------------
\3/ ________ 3/2 3/2
/ 2 / 2\ / 2\
/ x | x | | x |
/ 1 - -- 27*|1 - --| 9*|1 - --|
\/ 9 \ 9 / \ 9 /
$$\frac{2 x \cos{\left(2 x \right)}}{9 \left(1 - \frac{x^{2}}{9}\right)^{\frac{3}{2}}} - 8 \cos{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} - \frac{4 \sin{\left(2 x \right)}}{\sqrt{1 - \frac{x^{2}}{9}}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 9} - 1\right) \sin{\left(2 x \right)}}{27 \left(1 - \frac{x^{2}}{9}\right)^{\frac{3}{2}}}$$