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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
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- Integral Step by Step
- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of 5*x^4-7*x^2-x
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Derivative of 3x-x^2
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Derivative of 4*sqrt(3)*x/3
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Identical expressions
- t*arcsin(one -x)+arctg(x/ two)
- t multiply by arc sinus of (1 minus x) plus arctg(x divide by 2)
- t multiply by arc sinus of (one minus x) plus arctg(x divide by two)
- tarcsin(1-x)+arctg(x/2)
- tarcsin1-x+arctgx/2
- t*arcsin(1-x)+arctg(x divide by 2)
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Similar expressions
- t*arcsin(1+x)+arctg(x/2)
- t*arcsin(1-x)-arctg(x/2)
Derivative of t*arcsin(1-x)+arctg(x/2)
The solution
You have entered
[src]
/x\
t*asin(1 - x) + atan|-|
\2/
$$t \operatorname{asin}{\left(1 - x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}$$
t*asin(1 - x) + atan(x/2)
The first derivative
[src]
1 t ---------- - ----------------- / 2\ ______________ | x | / 2 2*|1 + --| \/ 1 - (1 - x) \ 4 /
$$- \frac{t}{\sqrt{1 - \left(1 - x\right)^{2}}} + \frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}$$
The second derivative
[src]
/ 4*x t*(-1 + x) \ -|--------- + -----------------| | 2 3/2| |/ 2\ / 2\ | \\4 + x / \1 - (1 - x) / /
$$- (\frac{t \left(x - 1\right)}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} + \frac{4 x}{\left(x^{2} + 4\right)^{2}})$$
The third derivative
[src]
2 2
4 t 16*x 3*t*(-1 + x)
- --------- - ----------------- + --------- - -----------------
2 3/2 3 5/2
/ 2\ / 2\ / 2\ / 2\
\4 + x / \1 - (1 - x) / \4 + x / \1 - (1 - x) /
$$- \frac{t}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} - \frac{3 t \left(x - 1\right)^{2}}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{5}{2}}} + \frac{16 x^{2}}{\left(x^{2} + 4\right)^{3}} - \frac{4}{\left(x^{2} + 4\right)^{2}}$$