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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of 2^3*sqrt(x)
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Derivative of 2ln(x)
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Derivative of 2-3*x-6*x^2
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Derivative of 1-2*x
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Identical expressions
- one / four (arctg(2x)^ four)
- 1 divide by 4(arctg(2x) to the power of 4)
- one divide by four (arctg(2x) to the power of four)
- 1/4(arctg(2x)4)
- 1/4arctg2x4
- 1/4(arctg(2x)⁴)
- 1/4arctg2x^4
- 1 divide by 4(arctg(2x)^4)
Derivative of 1/4(arctg(2x)^4)
The solution
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[src]
4
atan (2*x)
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4
$$\frac{\operatorname{atan}^{4}{\left(2 x \right)}}{4}$$
/ 4 \ d |atan (2*x)| --|----------| dx\ 4 /
$$\frac{d}{d x} \frac{\operatorname{atan}^{4}{\left(2 x \right)}}{4}$$
The first derivative
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3
2*atan (2*x)
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2
1 + 4*x
$$\frac{2 \operatorname{atan}^{3}{\left(2 x \right)}}{4 x^{2} + 1}$$
The second derivative
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2
-4*atan (2*x)*(-3 + 4*x*atan(2*x))
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2
/ 2\
\1 + 4*x /
$$- \frac{4 \cdot \left(4 x \operatorname{atan}{\left(2 x \right)} - 3\right) \operatorname{atan}^{2}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}}$$
The third derivative
[src]
/ 2 2 \
| 2 3 18*x*atan(2*x) 16*x *atan (2*x)|
16*|- atan (2*x) + -------- - -------------- + ----------------|*atan(2*x)
| 2 2 2 |
\ 1 + 4*x 1 + 4*x 1 + 4*x /
--------------------------------------------------------------------------
2
/ 2\
\1 + 4*x /
$$\frac{16 \cdot \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} - \frac{18 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{3}{4 x^{2} + 1}\right) \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}}$$
The graph