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How to use it?
- Derivative of:
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Derivative of 2x²
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Derivative of y=3x²+5x+4
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Derivative of x^3*cot(x)
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Derivative of sin(x)+3
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Identical expressions
- arctgx/(x^ seven + one)
- arctgx divide by (x to the power of 7 plus 1)
- arctgx divide by (x to the power of seven plus one)
- arctgx/(x7+1)
- arctgx/x7+1
- arctgx/(x⁷+1)
- arctgx/x^7+1
- arctgx divide by (x^7+1)
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Similar expressions
- arctgx/(x^7-1)
Derivative of arctgx/(x^7+1)
The solution
You have entered
[src]
acot(x) ------- 7 x + 1
$$\frac{\operatorname{acot}{\left(x \right)}}{x^{7} + 1}$$
acot(x)/(x^7 + 1)
The first derivative
[src]
6
1 7*x *acot(x)
- ----------------- - ------------
/ 2\ / 7 \ 2
\1 + x /*\x + 1/ / 7 \
\x + 1/
$$- \frac{7 x^{6} \operatorname{acot}{\left(x \right)}}{\left(x^{7} + 1\right)^{2}} - \frac{1}{\left(x^{2} + 1\right) \left(x^{7} + 1\right)}$$
The second derivative
[src]
/ / 7 \ \
| 4 | 7*x | |
| 7*x *|-3 + ------|*acot(x)|
| 5 | 7| |
| 1 7*x \ 1 + x / |
2*x*|--------- + ----------------- + --------------------------|
| 2 / 2\ / 7\ 7 |
|/ 2\ \1 + x /*\1 + x / 1 + x |
\\1 + x / /
----------------------------------------------------------------
7
1 + x
$$\frac{2 x \left(\frac{7 x^{5}}{\left(x^{2} + 1\right) \left(x^{7} + 1\right)} + \frac{7 x^{4} \left(\frac{7 x^{7}}{x^{7} + 1} - 3\right) \operatorname{acot}{\left(x \right)}}{x^{7} + 1} + \frac{1}{\left(x^{2} + 1\right)^{2}}\right)}{x^{7} + 1}$$
The third derivative
[src]
/ / 7 14 \ \
| 2 4 | 42*x 49*x | / 7 \|
| 4*x 21*x *|5 - ------ + ---------|*acot(x) 5 | 7*x ||
|-1 + ------ | 7 2| 21*x *|-3 + ------||
| 2 7 | 1 + x / 7\ | | 7||
| 1 + x 21*x \ \1 + x / / \ 1 + x /|
-2*|----------- + ------------------ + -------------------------------------- + -------------------|
| 2 2 7 / 2\ / 7\ |
| / 2\ / 2\ / 7\ 1 + x \1 + x /*\1 + x / |
\ \1 + x / \1 + x / *\1 + x / /
----------------------------------------------------------------------------------------------------
7
1 + x
$$- \frac{2 \left(\frac{21 x^{7}}{\left(x^{2} + 1\right)^{2} \left(x^{7} + 1\right)} + \frac{21 x^{5} \left(\frac{7 x^{7}}{x^{7} + 1} - 3\right)}{\left(x^{2} + 1\right) \left(x^{7} + 1\right)} + \frac{21 x^{4} \left(\frac{49 x^{14}}{\left(x^{7} + 1\right)^{2}} - \frac{42 x^{7}}{x^{7} + 1} + 5\right) \operatorname{acot}{\left(x \right)}}{x^{7} + 1} + \frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}}\right)}{x^{7} + 1}$$