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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 4/x
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Derivative of 1/2*x^2
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Derivative of e^(5*x)
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Derivative of x^2*e^(-x)
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Identical expressions
- (x(xarctgx- one)+arctgx)/ two
- (x(xarctgx minus 1) plus arctgx) divide by 2
- (x(xarctgx minus one) plus arctgx) divide by two
- xxarctgx-1+arctgx/2
- (x(xarctgx-1)+arctgx) divide by 2
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Similar expressions
- (x(xarctgx-1)-arctgx)/2
- (x(xarctgx+1)+arctgx)/2
Derivative of (x(xarctgx-1)+arctgx)/2
The solution
You have entered
[src]
x*(x*atan(x) - 1) + acot(x)
---------------------------
2
$$\frac{x \left(x \operatorname{atan}{\left(x \right)} - 1\right) + \operatorname{acot}{\left(x \right)}}{2}$$
(x*(x*atan(x) - 1) + acot(x))/2
The first derivative
[src]
/ x \
x*|------ + atan(x)|
| 2 |
1 1 \1 + x / x*atan(x)
- - - ---------- + -------------------- + ---------
2 / 2\ 2 2
2*\1 + x /
$$\frac{x \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{2} + \frac{x \operatorname{atan}{\left(x \right)}}{2} - \frac{1}{2} - \frac{1}{2 \left(x^{2} + 1\right)}$$
The second derivative
[src]
/ 2 \
| x |
x*|-1 + ------|
| 2|
x x \ 1 + x /
------ + --------- - --------------- + atan(x)
2 2 2
1 + x / 2\ 1 + x
\1 + x /
$$- \frac{x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{x}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right)^{2}} + \operatorname{atan}{\left(x \right)}$$
The third derivative
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/ 2 \
2 | x |
4*x *|-1 + ------|
2 2 | 2|
1 4*x 3*x \ 1 + x /
3 + ------ - --------- - ------ + ------------------
2 2 2 2
1 + x / 2\ 1 + x 1 + x
\1 + x /
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2
1 + x
$$\frac{\frac{4 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{3 x^{2}}{x^{2} + 1} - \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 3 + \frac{1}{x^{2} + 1}}{x^{2} + 1}$$