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How to use it?
- Derivative of:
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Derivative of (x^2+49)/x
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Derivative of sec2x
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Derivative of 6/x^4
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Derivative of x*e^x-e^x
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Identical expressions
- arctg^ seven (x^ two + one)
- arctg to the power of 7(x squared plus 1)
- arctg to the power of seven (x to the power of two plus one)
- arctg7(x2+1)
- arctg7x2+1
- arctg⁷(x²+1)
- arctg to the power of 7(x to the power of 2+1)
- arctg^7x^2+1
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Similar expressions
- arctg^7(x^2-1)
Derivative of arctg^7(x^2+1)
The solution
You have entered
[src]
7/ 2 \ atan \x + 1/
$$\operatorname{atan}^{7}{\left(x^{2} + 1 \right)}$$
atan(x^2 + 1)^7
The first derivative
[src]
6/ 2 \
14*x*atan \x + 1/
------------------
2
/ 2 \
1 + \x + 1/
$$\frac{14 x \operatorname{atan}^{6}{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2} + 1}$$
The second derivative
[src]
/ 2 2 / 2\ / 2\ \
5/ 2\ | 12*x 4*x *\1 + x /*atan\1 + x / / 2\|
14*atan \1 + x /*|------------- - -------------------------- + atan\1 + x /|
| 2 2 |
| / 2\ / 2\ |
\1 + \1 + x / 1 + \1 + x / /
----------------------------------------------------------------------------
2
/ 2\
1 + \1 + x /
$$\frac{14 \left(- \frac{4 x^{2} \left(x^{2} + 1\right) \operatorname{atan}{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2} + 1} + \frac{12 x^{2}}{\left(x^{2} + 1\right)^{2} + 1} + \operatorname{atan}{\left(x^{2} + 1 \right)}\right) \operatorname{atan}^{5}{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2} + 1}$$
The third derivative
[src]
/ 2 \
| 2 2 / 2\ / 2\ 2 / 2\ 2/ 2\|
4/ 2\ | / 2\ 2/ 2\ / 2\ 2 2/ 2\ 30*x 36*x *\1 + x /*atan\1 + x / 8*x *\1 + x / *atan \1 + x /|
56*x*atan \1 + x /*|9*atan\1 + x / - 3*atan \1 + x /*\1 + x / - 2*x *atan \1 + x / + ------------- - --------------------------- + ----------------------------|
| 2 2 2 |
| / 2\ / 2\ / 2\ |
\ 1 + \1 + x / 1 + \1 + x / 1 + \1 + x / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\
| / 2\ |
\1 + \1 + x / /
$$\frac{56 x \left(\frac{8 x^{2} \left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2} + 1} - \frac{36 x^{2} \left(x^{2} + 1\right) \operatorname{atan}{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2} + 1} - 2 x^{2} \operatorname{atan}^{2}{\left(x^{2} + 1 \right)} + \frac{30 x^{2}}{\left(x^{2} + 1\right)^{2} + 1} - 3 \left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x^{2} + 1 \right)} + 9 \operatorname{atan}{\left(x^{2} + 1 \right)}\right) \operatorname{atan}^{4}{\left(x^{2} + 1 \right)}}{\left(\left(x^{2} + 1\right)^{2} + 1\right)^{2}}$$