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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 sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of cot(x)/x
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Derivative of cos(x)/e^x
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Derivative of asin(x/2)
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Identical expressions
- arccot(x)/(x^(one / three))
- arc cotangent of (x) divide by (x to the power of (1 divide by 3))
- arc cotangent of (x) divide by (x to the power of (one divide by three))
- arccot(x)/(x(1/3))
- arccotx/x1/3
- arccotx/x^1/3
- arccot(x) divide by (x^(1 divide by 3))
Derivative of arccot(x)/(x^(1/3))
The solution
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[src]
acot(x) ------- 3 ___ \/ x
$$\frac{\operatorname{acot}{\left(x \right)}}{\sqrt[3]{x}}$$
d /acot(x)\ --|-------| dx| 3 ___ | \ \/ x /
$$\frac{d}{d x} \frac{\operatorname{acot}{\left(x \right)}}{\sqrt[3]{x}}$$
The first derivative
[src]
1 acot(x) - -------------- - ------- 3 ___ / 2\ 4/3 \/ x *\1 + x / 3*x
$$- \frac{1}{\sqrt[3]{x} \left(x^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x \right)}}{3 x^{\frac{4}{3}}}$$
The second derivative
[src]
/ 2/3 \ | x 1 2*acot(x)| 2*|--------- + --------------- + ---------| | 2 4/3 / 2\ 7/3 | |/ 2\ 3*x *\1 + x / 9*x | \\1 + x / /
$$2 \left(\frac{x^{\frac{2}{3}}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{3 x^{\frac{4}{3}} \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)}}{9 x^{\frac{7}{3}}}\right)$$
The third derivative
[src]
/ 2 \
| 4*x |
| -1 + ------ |
| 2 |
| 1 1 + x 2 14*acot(x)|
-2*|--------- + ----------- + ------------- + ----------|
| 2 2 2 / 2\ 3 |
|/ 2\ / 2\ 3*x *\1 + x / 27*x |
\\1 + x / \1 + x / /
---------------------------------------------------------
3 ___
\/ x
$$- \frac{2 \left(\frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{14 \operatorname{acot}{\left(x \right)}}{27 x^{3}} + \frac{2}{3 x^{2} \left(x^{2} + 1\right)}\right)}{\sqrt[3]{x}}$$
The graph