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- Derivative of:
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Derivative of (-2)/x^3
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Derivative of 3^-x
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Derivative of 2*x/(x^2+4)
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Derivative of f(x)=4x²-2x
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Identical expressions
- arccos^ four (ln(2x)- one)
- arc co sinus of e of to the power of 4(ln(2x) minus 1)
- arc co sinus of e of to the power of four (ln(2x) minus one)
- arccos4(ln(2x)-1)
- arccos4ln2x-1
- arccos⁴(ln(2x)-1)
- arccos^4ln2x-1
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Similar expressions
- arccos^4(ln(2x)+1)
Derivative of arccos^4(ln(2x)-1)
The solution
You have entered
[src]
4 acos (log(2*x) - 1)
$$\operatorname{acos}^{4}{\left(\log{\left(2 x \right)} - 1 \right)}$$
acos(log(2*x) - 1)^4
The first derivative
[src]
3
-4*acos (log(2*x) - 1)
--------------------------
_____________________
/ 2
x*\/ 1 - (log(2*x) - 1)
$$- \frac{4 \operatorname{acos}^{3}{\left(\log{\left(2 x \right)} - 1 \right)}}{x \sqrt{1 - \left(\log{\left(2 x \right)} - 1\right)^{2}}}$$
The second derivative
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2 / 3 acos(-1 + log(2*x)) (-1 + log(2*x))*acos(-1 + log(2*x))\
4*acos (-1 + log(2*x))*|- --------------------- + ------------------------- - -----------------------------------|
| 2 ______________________ 3/2 |
| -1 + (-1 + log(2*x)) / 2 / 2\ |
\ \/ 1 - (-1 + log(2*x)) \1 - (-1 + log(2*x)) / /
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2
x
$$\frac{4 \left(- \frac{3}{\left(\log{\left(2 x \right)} - 1\right)^{2} - 1} + \frac{\operatorname{acos}{\left(\log{\left(2 x \right)} - 1 \right)}}{\sqrt{1 - \left(\log{\left(2 x \right)} - 1\right)^{2}}} - \frac{\left(\log{\left(2 x \right)} - 1\right) \operatorname{acos}{\left(\log{\left(2 x \right)} - 1 \right)}}{\left(1 - \left(\log{\left(2 x \right)} - 1\right)^{2}\right)^{\frac{3}{2}}}\right) \operatorname{acos}^{2}{\left(\log{\left(2 x \right)} - 1 \right)}}{x^{2}}$$
The third derivative
[src]
/ 2 2 2 2 2 \
| 6 acos (-1 + log(2*x)) 2*acos (-1 + log(2*x)) 9*acos(-1 + log(2*x)) 3*(-1 + log(2*x)) *acos (-1 + log(2*x)) 3*acos (-1 + log(2*x))*(-1 + log(2*x)) 9*(-1 + log(2*x))*acos(-1 + log(2*x))|
4*|- ------------------------- - ------------------------- - ------------------------- + --------------------- - --------------------------------------- + -------------------------------------- + -------------------------------------|*acos(-1 + log(2*x))
| 3/2 3/2 ______________________ 2 5/2 3/2 2 |
| / 2\ / 2\ / 2 -1 + (-1 + log(2*x)) / 2\ / 2\ / 2\ |
\ \1 - (-1 + log(2*x)) / \1 - (-1 + log(2*x)) / \/ 1 - (-1 + log(2*x)) \1 - (-1 + log(2*x)) / \1 - (-1 + log(2*x)) / \-1 + (-1 + log(2*x)) / /
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3
x
$$\frac{4 \left(\frac{9 \operatorname{acos}{\left(\log{\left(2 x \right)} - 1 \right)}}{\left(\log{\left(2 x \right)} - 1\right)^{2} - 1} + \frac{9 \left(\log{\left(2 x \right)} - 1\right) \operatorname{acos}{\left(\log{\left(2 x \right)} - 1 \right)}}{\left(\left(\log{\left(2 x \right)} - 1\right)^{2} - 1\right)^{2}} - \frac{2 \operatorname{acos}^{2}{\left(\log{\left(2 x \right)} - 1 \right)}}{\sqrt{1 - \left(\log{\left(2 x \right)} - 1\right)^{2}}} + \frac{3 \left(\log{\left(2 x \right)} - 1\right) \operatorname{acos}^{2}{\left(\log{\left(2 x \right)} - 1 \right)}}{\left(1 - \left(\log{\left(2 x \right)} - 1\right)^{2}\right)^{\frac{3}{2}}} - \frac{\operatorname{acos}^{2}{\left(\log{\left(2 x \right)} - 1 \right)}}{\left(1 - \left(\log{\left(2 x \right)} - 1\right)^{2}\right)^{\frac{3}{2}}} - \frac{6}{\left(1 - \left(\log{\left(2 x \right)} - 1\right)^{2}\right)^{\frac{3}{2}}} - \frac{3 \left(\log{\left(2 x \right)} - 1\right)^{2} \operatorname{acos}^{2}{\left(\log{\left(2 x \right)} - 1 \right)}}{\left(1 - \left(\log{\left(2 x \right)} - 1\right)^{2}\right)^{\frac{5}{2}}}\right) \operatorname{acos}{\left(\log{\left(2 x \right)} - 1 \right)}}{x^{3}}$$