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How to use it?
- Derivative of:
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Derivative of x^7*e^x
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Derivative of 2/sqrt(x)
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Derivative of x*e^(1/x)
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Derivative of x*e^x^2
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Identical expressions
- xarccos(x/ four)+sqrt(sixteen -x^ two)
- xarc co sinus of e of (x divide by 4) plus square root of (16 minus x squared )
- xarc co sinus of e of (x divide by four) plus square root of (sixteen minus x to the power of two)
- xarccos(x/4)+√(16-x^2)
- xarccos(x/4)+sqrt(16-x2)
- xarccosx/4+sqrt16-x2
- xarccos(x/4)+sqrt(16-x²)
- xarccos(x/4)+sqrt(16-x to the power of 2)
- xarccosx/4+sqrt16-x^2
- xarccos(x divide by 4)+sqrt(16-x^2)
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Similar expressions
- xarccos(x/4)+sqrt(16+x^2)
- xarccos(x/4)-sqrt(16-x^2)
Derivative of xarccos(x/4)+sqrt(16-x^2)
The solution
You have entered
[src]
_________
/x\ / 2
x*acos|-| + \/ 16 - x
\4/
$$x \operatorname{acos}{\left(\frac{x}{4} \right)} + \sqrt{16 - x^{2}}$$
x*acos(x/4) + sqrt(16 - x^2)
The first derivative
[src]
x x /x\
- ------------ - --------------- + acos|-|
_________ ________ \4/
/ 2 / 2
\/ 16 - x / x
4* / 1 - --
\/ 16
$$- \frac{x}{\sqrt{16 - x^{2}}} - \frac{x}{4 \sqrt{1 - \frac{x^{2}}{16}}} + \operatorname{acos}{\left(\frac{x}{4} \right)}$$
The second derivative
[src]
/ 2 2 \ | 1 1 x x | -|------------ + --------------- + ------------ + --------------| | _________ ________ 3/2 3/2| | / 2 / 2 / 2\ / 2\ | |\/ 16 - x / x \16 - x / | x | | | 2* / 1 - -- 64*|1 - --| | \ \/ 16 \ 16/ /
$$- (\frac{x^{2}}{\left(16 - x^{2}\right)^{\frac{3}{2}}} + \frac{x^{2}}{64 \left(1 - \frac{x^{2}}{16}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{16 - x^{2}}} + \frac{1}{2 \sqrt{1 - \frac{x^{2}}{16}}})$$
The third derivative
[src]
/ 2 2 \ | 3 1 3*x 3*x | -x*|------------ + -------------- + ------------ + ----------------| | 3/2 3/2 5/2 5/2| |/ 2\ / 2\ / 2\ / 2\ | |\16 - x / | x | \16 - x / | x | | | 16*|1 - --| 1024*|1 - --| | \ \ 16/ \ 16/ /
$$- x \left(\frac{3 x^{2}}{\left(16 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x^{2}}{1024 \left(1 - \frac{x^{2}}{16}\right)^{\frac{5}{2}}} + \frac{3}{\left(16 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{16 \left(1 - \frac{x^{2}}{16}\right)^{\frac{3}{2}}}\right)$$