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- Derivative of a implicit defined function
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- Derivative of:
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Derivative of e^(5*x)
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Derivative of x^2+x+1
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Derivative of (x^2+1)^2
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Derivative of sqrt(2*x)
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Identical expressions
- (acot(x))^x
- ( arcco tangent of gent of (x)) to the power of x
- (acot(x))x
- acotxx
- acotx^x
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Similar expressions
- (arccot(x))^x
- (arccotx)^x
Derivative of (acot(x))^x
The solution
You have entered
[src]
x acot (x)
$$\operatorname{acot}^{x}{\left(x \right)}$$
d / x \ --\acot (x)/ dx
$$\frac{d}{d x} \operatorname{acot}^{x}{\left(x \right)}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
x / x \
acot (x)*|- ---------------- + log(acot(x))|
| / 2\ |
\ \1 + x /*acot(x) /
$$\left(- \frac{x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \log{\left(\operatorname{acot}{\left(x \right)} \right)}\right) \operatorname{acot}^{x}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
| 2*x x |
| 2 - ------ + ----------------|
| 2 2 / 2\ |
x |/ x \ 1 + x \1 + x /*acot(x)|
acot (x)*||-log(acot(x)) + ----------------| - -----------------------------|
|| / 2\ | / 2\ |
\\ \1 + x /*acot(x)/ \1 + x /*acot(x) /
$$\left(\left(\frac{x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \log{\left(\operatorname{acot}{\left(x \right)} \right)}\right)^{2} - \frac{- \frac{2 x^{2}}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 2}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \operatorname{acot}^{x}{\left(x \right)}$$
The third derivative
[src]
/ 3 2 / 2 \\
| 3 8*x 6*x 2*x / x \ | 2*x x ||
| -8*x + ------- + ------ - ---------------- + ----------------- 3*|-log(acot(x)) + ----------------|*|2 - ------ + ----------------||
| 3 acot(x) 2 / 2\ / 2\ 2 | / 2\ | | 2 / 2\ ||
x | / x \ 1 + x \1 + x /*acot(x) \1 + x /*acot (x) \ \1 + x /*acot(x)/ \ 1 + x \1 + x /*acot(x)/|
acot (x)*|- |-log(acot(x)) + ----------------| - -------------------------------------------------------------- + --------------------------------------------------------------------|
| | / 2\ | 2 / 2\ |
| \ \1 + x /*acot(x)/ / 2\ \1 + x /*acot(x) |
\ \1 + x / *acot(x) /
$$\left(- \left(\frac{x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \log{\left(\operatorname{acot}{\left(x \right)} \right)}\right)^{3} + \frac{3 \left(\frac{x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \log{\left(\operatorname{acot}{\left(x \right)} \right)}\right) \left(- \frac{2 x^{2}}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 2\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{\frac{8 x^{3}}{x^{2} + 1} - \frac{6 x^{2}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 8 x + \frac{2 x}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} + \frac{3}{\operatorname{acot}{\left(x \right)}}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}}\right) \operatorname{acot}^{x}{\left(x \right)}$$
The graph