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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 x^(4/5)
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Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
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Derivative of x^3+2
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Derivative of x^2-7*x
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Identical expressions
- arctan(x)+arctan(one /x)
- arc tangent of (x) plus arc tangent of (1 divide by x)
- arc tangent of (x) plus arc tangent of (one divide by x)
- arctanx+arctan1/x
- arctan(x)+arctan(1 divide by x)
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Similar expressions
- arctan(x)-arctan(1/x)
Derivative of arctan(x)+arctan(1/x)
The solution
You have entered
[src]
/1\
atan(x) + atan|-|
\x/
$$\operatorname{atan}{\left(\frac{1}{x} \right)} + \operatorname{atan}{\left(x \right)}$$
atan(x) + atan(1/x)
The first derivative
[src]
1 1
------ - -----------
2 2 / 1 \
1 + x x *|1 + --|
| 2|
\ x /
$$\frac{1}{x^{2} + 1} - \frac{1}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}$$
The second derivative
[src]
/ 1 x 1 \ 2*|----------- - --------- - ------------| | 3 / 1 \ 2 2| |x *|1 + --| / 2\ 5 / 1 \ | | | 2| \1 + x / x *|1 + --| | | \ x / | 2| | \ \ x / /
$$2 \left(- \frac{x}{\left(x^{2} + 1\right)^{2}} + \frac{1}{x^{3} \left(1 + \frac{1}{x^{2}}\right)} - \frac{1}{x^{5} \left(1 + \frac{1}{x^{2}}\right)^{2}}\right)$$
The third derivative
[src]
/ 2 \ | 1 4 3 4*x 7 | 2*|- --------- - ------------ - ----------- + --------- + ------------| | 2 3 4 / 1 \ 3 2| | / 2\ 8 / 1 \ x *|1 + --| / 2\ 6 / 1 \ | | \1 + x / x *|1 + --| | 2| \1 + x / x *|1 + --| | | | 2| \ x / | 2| | \ \ x / \ x / /
$$2 \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} - \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{3}{x^{4} \left(1 + \frac{1}{x^{2}}\right)} + \frac{7}{x^{6} \left(1 + \frac{1}{x^{2}}\right)^{2}} - \frac{4}{x^{8} \left(1 + \frac{1}{x^{2}}\right)^{3}}\right)$$
The graph