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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 x^12
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Derivative of -e^x
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Derivative of e^(2-x)
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Derivative of x^2-4*x
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Identical expressions
- arcctg(two x*2^(x))
- arcctg(2x multiply by 2 to the power of (x))
- arcctg(two x multiply by 2 to the power of (x))
- arcctg(2x*2(x))
- arcctg2x*2x
- arcctg(2x2^(x))
- arcctg(2x2(x))
- arcctg2x2x
- arcctg2x2^x
Derivative of arcctg(2x*2^(x))
The solution
You have entered
[src]
/ x\ acot\2*x*2 /
$$\operatorname{acot}{\left(2^{x} 2 x \right)}$$
acot((2*x)*2^x)
The first derivative
[src]
/ x x \
-\2*2 + 2*x*2 *log(2)/
------------------------
2*x 2
1 + 4*2 *x
$$- \frac{2 \cdot 2^{x} x \log{\left(2 \right)} + 2 \cdot 2^{x}}{4 \cdot 2^{2 x} x^{2} + 1}$$
The second derivative
[src]
/ 2*x 2\
x | 8*x*2 *(1 + x*log(2)) |
2*2 *|-(2 + x*log(2))*log(2) + ------------------------|
| 2*x 2 |
\ 1 + 4*2 *x /
--------------------------------------------------------
2*x 2
1 + 4*2 *x
$$\frac{2 \cdot 2^{x} \left(\frac{8 \cdot 2^{2 x} x \left(x \log{\left(2 \right)} + 1\right)^{2}}{4 \cdot 2^{2 x} x^{2} + 1} - \left(x \log{\left(2 \right)} + 2\right) \log{\left(2 \right)}\right)}{4 \cdot 2^{2 x} x^{2} + 1}$$
The third derivative
[src]
/ 4*x 2 3 2*x / 2 2 \ 2*x \
x | 2 128*2 *x *(1 + x*log(2)) 8*2 *(1 + x*log(2))*\1 + 2*x *log (2) + 4*x*log(2)/ 16*x*2 *(1 + x*log(2))*(2 + x*log(2))*log(2)|
2*2 *|- log (2)*(3 + x*log(2)) - --------------------------- + ----------------------------------------------------- + ----------------------------------------------|
| 2 2*x 2 2*x 2 |
| / 2*x 2\ 1 + 4*2 *x 1 + 4*2 *x |
\ \1 + 4*2 *x / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
2*x 2
1 + 4*2 *x
$$\frac{2 \cdot 2^{x} \left(- \frac{128 \cdot 2^{4 x} x^{2} \left(x \log{\left(2 \right)} + 1\right)^{3}}{\left(4 \cdot 2^{2 x} x^{2} + 1\right)^{2}} + \frac{16 \cdot 2^{2 x} x \left(x \log{\left(2 \right)} + 1\right) \left(x \log{\left(2 \right)} + 2\right) \log{\left(2 \right)}}{4 \cdot 2^{2 x} x^{2} + 1} + \frac{8 \cdot 2^{2 x} \left(x \log{\left(2 \right)} + 1\right) \left(2 x^{2} \log{\left(2 \right)}^{2} + 4 x \log{\left(2 \right)} + 1\right)}{4 \cdot 2^{2 x} x^{2} + 1} - \left(x \log{\left(2 \right)} + 3\right) \log{\left(2 \right)}^{2}\right)}{4 \cdot 2^{2 x} x^{2} + 1}$$