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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
-
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 (3*x-5)^6
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Identical expressions
- arccos(sin(x)/x)
- arc co sinus of e of ( sinus of (x) divide by x)
- arccossinx/x
- arccos(sin(x) divide by x)
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Similar expressions
- arccos(sinx/x)
Derivative of arccos(sin(x)/x)
The solution
You have entered
[src]
/sin(x)\
acos|------|
\ x /
$$\operatorname{acos}{\left(\frac{\sin{\left(x \right)}}{x} \right)}$$
acos(sin(x)/x)
The first derivative
[src]
/cos(x) sin(x)\
-|------ - ------|
| x 2 |
\ x /
-------------------
_____________
/ 2
/ sin (x)
/ 1 - -------
/ 2
\/ x
$$- \frac{\frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}}{\sqrt{1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}}}$$
The second derivative
[src]
2
/ sin(x) \
|- ------ + cos(x)| *sin(x)
2*sin(x) 2*cos(x) \ x /
- -------- + -------- - --------------------------- + sin(x)
2 x / 2 \
x 2 | sin (x)|
x *|1 - -------|
| 2 |
\ x /
------------------------------------------------------------
_____________
/ 2
/ sin (x)
x* / 1 - -------
/ 2
\/ x
$$\frac{\sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{2 \sin{\left(x \right)}}{x^{2}} - \frac{\left(\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin{\left(x \right)}}{x^{2} \left(1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right)}}{x \sqrt{1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}}}$$
The third derivative
[src]
/ 2 \
/ sin(x) \ | 2 2 3*sin (x) 4*cos(x)*sin(x)| 3 / sin(x) \ / 2*sin(x) 2*cos(x) \
|- ------ + cos(x)|*|sin (x) - cos (x) - --------- + ---------------| / sin(x) \ 2 2*|- ------ + cos(x)|*|- -------- + -------- + sin(x)|*sin(x)
\ x / | 2 x | 3*|- ------ + cos(x)| *sin (x) \ x / | 2 x |
6*cos(x) 3*sin(x) 6*sin(x) \ x / \ x / \ x /
- -------- - -------- + -------- + --------------------------------------------------------------------- - ------------------------------ + ------------------------------------------------------------- + cos(x)
2 x 3 / 2 \ 2 / 2 \
x x 2 | sin (x)| / 2 \ 2 | sin (x)|
x *|1 - -------| 4 | sin (x)| x *|1 - -------|
| 2 | x *|1 - -------| | 2 |
\ x / | 2 | \ x /
\ x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________
/ 2
/ sin (x)
x* / 1 - -------
/ 2
\/ x
$$\frac{\cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{6 \cos{\left(x \right)}}{x^{2}} + \frac{2 \left(\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}\right) \left(\sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{2 \sin{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x^{2} \left(1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right)} + \frac{\left(\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}\right) \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{3 \sin^{2}{\left(x \right)}}{x^{2}}\right)}{x^{2} \left(1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right)} + \frac{6 \sin{\left(x \right)}}{x^{3}} - \frac{3 \left(\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}\right)^{3} \sin^{2}{\left(x \right)}}{x^{4} \left(1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right)^{2}}}{x \sqrt{1 - \frac{\sin^{2}{\left(x \right)}}{x^{2}}}}$$