Mister Exam
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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:
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Derivative of 1/x^6
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Derivative of x+lnx
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Derivative of x^2-4*x+3
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Derivative of -(x^2+324)/x
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Identical expressions
- acos(two ^(x- one))
- arc co sinus of e of ine of (2 to the power of (x minus 1))
- arc co sinus of e of ine of (two to the power of (x minus one))
- acos(2(x-1))
- acos2x-1
- acos2^x-1
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Similar expressions
- acos(2^(x+1))
- arccos(2^(x-1))
Derivative of acos(2^(x-1))
The solution
You have entered
[src]
/ x - 1\ acos\2 /
$$\operatorname{acos}{\left(2^{x - 1} \right)}$$
acos(2^(x - 1))
The first derivative
[src]
x - 1 -2 *log(2) ------------------ _______________ / -2 + 2*x \/ 1 - 2
$$- \frac{2^{x - 1} \log{\left(2 \right)}}{\sqrt{1 - 2^{2 x - 2}}}$$
The second derivative
[src]
/ 2*x \
x 2 | 2 |
-2 *log (2)*|4 + --------|
| 2*x|
| 2 |
| 1 - ----|
\ 4 /
---------------------------
__________
/ 2*x
/ 2
8* / 1 - ----
\/ 4
$$- \frac{2^{x} \left(\frac{2^{2 x}}{1 - \frac{2^{2 x}}{4}} + 4\right) \log{\left(2 \right)}^{2}}{8 \sqrt{1 - \frac{2^{2 x}}{4}}}$$
The third derivative
[src]
/ 4*x 2*x \
x 3 | 3*2 16*2 |
-2 *log (2)*|16 + ----------- + --------|
| 2 2*x|
| / 2*x\ 2 |
| | 2 | 1 - ----|
| |1 - ----| 4 |
\ \ 4 / /
------------------------------------------
__________
/ 2*x
/ 2
32* / 1 - ----
\/ 4
$$- \frac{2^{x} \left(\frac{3 \cdot 2^{4 x}}{\left(1 - \frac{2^{2 x}}{4}\right)^{2}} + \frac{16 \cdot 2^{2 x}}{1 - \frac{2^{2 x}}{4}} + 16\right) \log{\left(2 \right)}^{3}}{32 \sqrt{1 - \frac{2^{2 x}}{4}}}$$