Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of (-2)/x^2
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Derivative of 2x^2-x
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Derivative of (cos(x))^sin(x)
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Derivative of y=3x^2
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Identical expressions
- (ln(arccos(one /sqrt(x))))
- (ln(arc co sinus of e of (1 divide by square root of (x))))
- (ln(arc co sinus of e of (one divide by square root of (x))))
- (ln(arccos(1/√(x))))
- lnarccos1/sqrtx
- (ln(arccos(1 divide by sqrt(x))))
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Similar expressions
- y=ln(arccos(1/sqrt(x)))
- ln(arccos(1)/(sqrt(x)))
- ln*(arccos*1/sqrt(x))
Derivative of (ln(arccos(1/sqrt(x))))
The solution
You have entered
[src]
/ / 1 \\ log|acos|-----|| | | ___|| \ \\/ x //
$$\log{\left(\operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)} \right)}$$
log(acos(1/(sqrt(x))))
The first derivative
[src]
1
------------------------------
_______
3/2 / 1 / 1 \
2*x * / 1 - - *acos|-----|
\/ x | ___|
\\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{x}} \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}$$
The second derivative
[src]
/ 1 3 1 \
-|--------------- + ---------------- + ----------------------|
| 3/2 _______ 3 / 1\ / 1 \|
| 7/2 / 1\ 5/2 / 1 x *|1 - -|*acos|-----||
|x *|1 - -| x * / 1 - - \ x/ | ___||
\ \ x/ \/ x \\/ x //
---------------------------------------------------------------
/ 1 \
4*acos|-----|
| ___|
\\/ x /
$$- \frac{\frac{1}{x^{3} \left(1 - \frac{1}{x}\right) \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{\frac{5}{2}} \sqrt{1 - \frac{1}{x}}} + \frac{1}{x^{\frac{7}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}}}}{4 \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}$$
The third derivative
[src]
3 10 15 2 3 9
---------------- + --------------- + ---------------- + ---------------------------- + ----------------------- + ----------------------
5/2 3/2 _______ 3/2 2 4 / 1\ / 1 \
11/2 / 1\ 9/2 / 1\ 7/2 / 1 9/2 / 1\ 2/ 1 \ 5 / 1\ / 1 \ x *|1 - -|*acos|-----|
x *|1 - -| x *|1 - -| x * / 1 - - x *|1 - -| *acos |-----| x *|1 - -| *acos|-----| \ x/ | ___|
\ x/ \ x/ \/ x \ x/ | ___| \ x/ | ___| \\/ x /
\\/ x / \\/ x /
---------------------------------------------------------------------------------------------------------------------------------------
/ 1 \
8*acos|-----|
| ___|
\\/ x /
$$\frac{\frac{9}{x^{4} \left(1 - \frac{1}{x}\right) \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{5} \left(1 - \frac{1}{x}\right)^{2} \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{15}{x^{\frac{7}{2}} \sqrt{1 - \frac{1}{x}}} + \frac{10}{x^{\frac{9}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}}} + \frac{2}{x^{\frac{9}{2}} \left(1 - \frac{1}{x}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(\frac{1}{\sqrt{x}} \right)}} + \frac{3}{x^{\frac{11}{2}} \left(1 - \frac{1}{x}\right)^{\frac{5}{2}}}}{8 \operatorname{acos}{\left(\frac{1}{\sqrt{x}} \right)}}$$