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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
- Derivative of log(2)
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Derivative of 1/(x-1)
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Derivative of x*ctgx
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Derivative of sin(lnx)
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Identical expressions
- arctg(x^ two -4x)
- arctg(x squared minus 4x)
- arctg(x to the power of two minus 4x)
- arctg(x2-4x)
- arctgx2-4x
- arctg(x²-4x)
- arctg(x to the power of 2-4x)
- arctgx^2-4x
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Similar expressions
- arctg(x^2+4x)
Derivative of arctg(x^2-4x)
The solution
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[src]
/ 2 \ atan\x - 4*x/
$$\operatorname{atan}{\left(x^{2} - 4 x \right)}$$
d / / 2 \\ --\atan\x - 4*x// dx
$$\frac{d}{d x} \operatorname{atan}{\left(x^{2} - 4 x \right)}$$
The first derivative
[src]
-4 + 2*x
---------------
2
/ 2 \
1 + \x - 4*x/
$$\frac{2 x - 4}{\left(x^{2} - 4 x\right)^{2} + 1}$$
The second derivative
[src]
/ 2 \
| 4*x*(-2 + x) *(-4 + x)|
2*|1 - ----------------------|
| 2 2 |
\ 1 + x *(-4 + x) /
------------------------------
2 2
1 + x *(-4 + x)
$$\frac{2 \left(- \frac{4 x \left(x - 4\right) \left(x - 2\right)^{2}}{x^{2} \left(x - 4\right)^{2} + 1} + 1\right)}{x^{2} \left(x - 4\right)^{2} + 1}$$
The third derivative
[src]
/ 2 2 2\
| 2 8*x *(-4 + x) *(-2 + x) |
8*(-2 + x)*|- 2*(-2 + x) - 3*x*(-4 + x) + ------------------------|
| 2 2 |
\ 1 + x *(-4 + x) /
--------------------------------------------------------------------
2
/ 2 2\
\1 + x *(-4 + x) /
$$\frac{8 \left(x - 2\right) \left(\frac{8 x^{2} \left(x - 4\right)^{2} \left(x - 2\right)^{2}}{x^{2} \left(x - 4\right)^{2} + 1} - 3 x \left(x - 4\right) - 2 \left(x - 2\right)^{2}\right)}{\left(x^{2} \left(x - 4\right)^{2} + 1\right)^{2}}$$
The graph