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- Derivative of:
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Derivative of sin(x)+cos(x)
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Derivative of cos(x)^2
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Derivative of sin(x^3)
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Derivative of log(x)^2
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Identical expressions
- arctg((one -x)/(4x- one))
- arctg((1 minus x) divide by (4x minus 1))
- arctg((one minus x) divide by (4x minus one))
- arctg1-x/4x-1
- arctg((1-x) divide by (4x-1))
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Similar expressions
- arctg((1-x)/(4x+1))
- arctg((1+x)/(4x-1))
Derivative of arctg((1-x)/(4x-1))
The solution
You have entered
[src]
/ 1 - x \
atan|-------|
\4*x - 1/
$$\operatorname{atan}{\left(\frac{1 - x}{4 x - 1} \right)}$$
atan((1 - x)/(4*x - 1))
The first derivative
[src]
1 4*(1 - x)
- ------- - ----------
4*x - 1 2
(4*x - 1)
----------------------
2
(1 - x)
1 + ----------
2
(4*x - 1)
$$\frac{- \frac{4 \left(1 - x\right)}{\left(4 x - 1\right)^{2}} - \frac{1}{4 x - 1}}{\frac{\left(1 - x\right)^{2}}{\left(4 x - 1\right)^{2}} + 1}$$
The second derivative
[src]
/ / 4*(-1 + x)\ \
| (-1 + x)*|-1 + ----------| |
/ 4*(-1 + x)\ | \ -1 + 4*x / |
2*|-1 + ----------|*|-4 + ----------------------------|
\ -1 + 4*x / | / 2 \ |
| | (-1 + x) | |
| |1 + -----------|*(-1 + 4*x)|
| | 2| |
\ \ (-1 + 4*x) / /
-------------------------------------------------------
/ 2 \
| (-1 + x) | 2
|1 + -----------|*(-1 + 4*x)
| 2|
\ (-1 + 4*x) /
$$\frac{2 \left(\frac{4 \left(x - 1\right)}{4 x - 1} - 1\right) \left(\frac{\left(x - 1\right) \left(\frac{4 \left(x - 1\right)}{4 x - 1} - 1\right)}{\left(4 x - 1\right) \left(\frac{\left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} + 1\right)} - 4\right)}{\left(4 x - 1\right)^{2} \left(\frac{\left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} + 1\right)}$$
The third derivative
[src]
/ 2 \
| 16*(-1 + x) 48*(-1 + x) 2|
| 1 - ----------- + ------------ / 4*(-1 + x)\ 2 / 4*(-1 + x)\ |
| -1 + 4*x 2 16*(-1 + x)*|-1 + ----------| 4*(-1 + x) *|-1 + ----------| |
/ 4*(-1 + x)\ | (-1 + 4*x) \ -1 + 4*x / \ -1 + 4*x / |
2*|-1 + ----------|*|48 - ------------------------------ - ----------------------------- + ------------------------------|
\ -1 + 4*x / | 2 / 2 \ 2 |
| (-1 + x) | (-1 + x) | / 2 \ |
| 1 + ----------- |1 + -----------|*(-1 + 4*x) | (-1 + x) | 2|
| 2 | 2| |1 + -----------| *(-1 + 4*x) |
| (-1 + 4*x) \ (-1 + 4*x) / | 2| |
\ \ (-1 + 4*x) / /
--------------------------------------------------------------------------------------------------------------------------
/ 2 \
| (-1 + x) | 3
|1 + -----------|*(-1 + 4*x)
| 2|
\ (-1 + 4*x) /
$$\frac{2 \left(\frac{4 \left(x - 1\right)}{4 x - 1} - 1\right) \left(\frac{4 \left(x - 1\right)^{2} \left(\frac{4 \left(x - 1\right)}{4 x - 1} - 1\right)^{2}}{\left(4 x - 1\right)^{2} \left(\frac{\left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} + 1\right)^{2}} - \frac{16 \left(x - 1\right) \left(\frac{4 \left(x - 1\right)}{4 x - 1} - 1\right)}{\left(4 x - 1\right) \left(\frac{\left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} + 1\right)} + 48 - \frac{\frac{48 \left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} - \frac{16 \left(x - 1\right)}{4 x - 1} + 1}{\frac{\left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} + 1}\right)}{\left(4 x - 1\right)^{3} \left(\frac{\left(x - 1\right)^{2}}{\left(4 x - 1\right)^{2}} + 1\right)}$$