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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 2^(3*x)
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Derivative of -2/x
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Derivative of sin(x)*cos(x)
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Derivative of 1/cos(x)
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Identical expressions
- acot(x^ two /a+pi*k)
- arcco tangent of gent of (x squared divide by a plus Pi multiply by k)
- arcco tangent of gent of (x to the power of two divide by a plus Pi multiply by k)
- acot(x2/a+pi*k)
- acotx2/a+pi*k
- acot(x²/a+pi*k)
- acot(x to the power of 2/a+pi*k)
- acot(x^2/a+pik)
- acot(x2/a+pik)
- acotx2/a+pik
- acotx^2/a+pik
- acot(x^2 divide by a+pi*k)
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Similar expressions
- acot(x^2/a-pi*k)
- arccot(x^2/a+pi*k)
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What you mean?
- acot(x^2/a + pi*k)
- acot(x^(2/a) + pi*k)
- acot(x^2/(a + pi*k))
- acot(x^2*k/(a + pi))
- acot(x^2/a + pi*k)
- acot(x*2/(a + pi*k))
- acot(x^2*k/(a + pi))
You entered:
acot(x^2/a+pi*k)
What you mean?
Derivative of acot(x^2/a+pi*k)
The solution
You have entered
[src]
/ 2 \
|x |
acot|-- + pi*k|
\a /
$$\operatorname{acot}{\left(\pi k + \frac{x^{2}}{a} \right)}$$
/ / 2 \\ d | |x || --|acot|-- + pi*k|| dx\ \a //
$$\frac{\partial}{\partial x} \operatorname{acot}{\left(\pi k + \frac{x^{2}}{a} \right)}$$
The first derivative
[src]
-2*x -------------------- / 2\ | / 2 \ | | |x | | a*|1 + |-- + pi*k| | \ \a / /
$$- \frac{2 x}{a \left(\left(\pi k + \frac{x^{2}}{a}\right)^{2} + 1\right)}$$
The second derivative
[src]
/ / 2\ \
| 2 | x | |
| 4*x *|pi*k + --| |
| \ a / |
2*|-1 + --------------------|
| / 2\|
| | / 2\ ||
| | | x | ||
| a*|1 + |pi*k + --| ||
\ \ \ a / //
-----------------------------
/ 2\
| / 2\ |
| | x | |
a*|1 + |pi*k + --| |
\ \ a / /
$$\frac{2 \left(\frac{4 x^{2} \left(\pi k + \frac{x^{2}}{a}\right)}{a \left(\left(\pi k + \frac{x^{2}}{a}\right)^{2} + 1\right)} - 1\right)}{a \left(\left(\pi k + \frac{x^{2}}{a}\right)^{2} + 1\right)}$$
The third derivative
[src]
/ 2 \
| / 2\ |
| 2 | x | |
| 2 8*x *|pi*k + --| |
| 5*x \ a / |
8*x*|3*pi*k + ---- - --------------------|
| a / 2\|
| | / 2\ ||
| | | x | ||
| a*|1 + |pi*k + --| ||
\ \ \ a / //
------------------------------------------
2
/ 2\
| / 2\ |
2 | | x | |
a *|1 + |pi*k + --| |
\ \ a / /
$$\frac{8 x \left(- \frac{8 x^{2} \left(\pi k + \frac{x^{2}}{a}\right)^{2}}{a \left(\left(\pi k + \frac{x^{2}}{a}\right)^{2} + 1\right)} + 3 \pi k + \frac{5 x^{2}}{a}\right)}{a^{2} \left(\left(\pi k + \frac{x^{2}}{a}\right)^{2} + 1\right)^{2}}$$