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 e^2*x
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Derivative of cos(x)^2
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Derivative of x^sin(x)
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Derivative of sin(x^3)
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Identical expressions
- arccos(x^ four - one)
- arc co sinus of e of (x to the power of 4 minus 1)
- arc co sinus of e of (x to the power of four minus one)
- arccos(x4-1)
- arccosx4-1
- arccos(x⁴-1)
- arccosx^4-1
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Similar expressions
- arccos(x^4+1)
Derivative of arccos(x^4-1)
The solution
You have entered
[src]
/ 4 \ acos\x - 1/
$$\operatorname{acos}{\left(x^{4} - 1 \right)}$$
acos(x^4 - 1)
The first derivative
[src]
3
-4*x
-------------------
_______________
/ 2
/ / 4 \
\/ 1 - \x - 1/
$$- \frac{4 x^{3}}{\sqrt{1 - \left(x^{4} - 1\right)^{2}}}$$
The second derivative
[src]
/ 4 / 4\\
2 | 4*x *\-1 + x /|
-4*x *|3 + --------------|
| 2|
| / 4\ |
\ 1 - \-1 + x / /
--------------------------
________________
/ 2
/ / 4\
\/ 1 - \-1 + x /
$$- \frac{4 x^{2} \left(\frac{4 x^{4} \left(x^{4} - 1\right)}{1 - \left(x^{4} - 1\right)^{2}} + 3\right)}{\sqrt{1 - \left(x^{4} - 1\right)^{2}}}$$
The third derivative
[src]
/ 2\
| 8 4 / 4\ 8 / 4\ |
| 8*x 18*x *\-1 + x / 24*x *\-1 + x / |
-8*x*|3 + -------------- + --------------- + -----------------|
| 2 2 2|
| / 4\ / 4\ / 2\ |
| 1 - \-1 + x / 1 - \-1 + x / | / 4\ | |
\ \1 - \-1 + x / / /
---------------------------------------------------------------
________________
/ 2
/ / 4\
\/ 1 - \-1 + x /
$$- \frac{8 x \left(\frac{8 x^{8}}{1 - \left(x^{4} - 1\right)^{2}} + \frac{24 x^{8} \left(x^{4} - 1\right)^{2}}{\left(1 - \left(x^{4} - 1\right)^{2}\right)^{2}} + \frac{18 x^{4} \left(x^{4} - 1\right)}{1 - \left(x^{4} - 1\right)^{2}} + 3\right)}{\sqrt{1 - \left(x^{4} - 1\right)^{2}}}$$