Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of sin(x/3)^(2)*cot(x/2)
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Derivative of atan(sqrt(x))
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Derivative of atan(2*x)
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Derivative of asin(1/x)
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Identical expressions
- arctg* one /x+arcctgx
- arctg multiply by 1 divide by x plus arcctgx
- arctg multiply by one divide by x plus arcctgx
- arctg1/x+arcctgx
- arctg*1 divide by x+arcctgx
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Similar expressions
- arctg*1/x-arcctgx
Derivative of arctg*1/x+arcctgx
The solution
You have entered
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atan(1) ------- + acot(x) x
$$\operatorname{acot}{\left(x \right)} + \frac{\operatorname{atan}{\left(1 \right)}}{x}$$
The first derivative
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1 atan(1)
- ------ - -------
2 2
1 + x x
$$- \frac{1}{x^{2} + 1} - \frac{\operatorname{atan}{\left(1 \right)}}{x^{2}}$$
The second derivative
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/ x atan(1)\ 2*|--------- + -------| | 2 3 | |/ 2\ x | \\1 + x / /
$$2 \left(\frac{x}{\left(x^{2} + 1\right)^{2}} + \frac{\operatorname{atan}{\left(1 \right)}}{x^{3}}\right)$$
The third derivative
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/ 2 \ | 1 4*x 3*atan(1)| 2*|--------- - --------- - ---------| | 2 3 4 | |/ 2\ / 2\ x | \\1 + x / \1 + x / /
$$2 \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{3 \operatorname{atan}{\left(1 \right)}}{x^{4}}\right)$$
6-я производная
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/ 3 5 \
| 16*x 3*x 3*atan(1) 16*x |
240*|- --------- + --------- + --------- + ---------|
| 5 4 7 6|
| / 2\ / 2\ x / 2\ |
\ \1 + x / \1 + x / \1 + x / /
$$240 \left(\frac{16 x^{5}}{\left(x^{2} + 1\right)^{6}} - \frac{16 x^{3}}{\left(x^{2} + 1\right)^{5}} + \frac{3 x}{\left(x^{2} + 1\right)^{4}} + \frac{3 \operatorname{atan}{\left(1 \right)}}{x^{7}}\right)$$
The graph