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How to use it?
- Derivative of:
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Derivative of f(x)=1
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Derivative of (x+8)^2
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Derivative of x^5-2*x
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Derivative of x^3-3
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Identical expressions
- abs(3x+ one)cbrt(one /(3x)+ one)
- abs(3x plus 1) cubic root of (1 divide by (3x) plus 1)
- abs(3x plus one) cubic root of (one divide by (3x) plus one)
- abs3x+1cbrt1/3x+1
- abs(3x+1)cbrt(1 divide by (3x)+1)
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Similar expressions
- abs(3x+1)cbrt(1/(3x)-1)
- abs(3x-1)cbrt(1/(3x)+1)
Derivative of abs(3x+1)cbrt(1/(3x)+1)
The solution
You have entered
[src]
___________
/ 1
|3*x + 1|*3 / 1*--- + 1
\/ 3*x
$$\sqrt[3]{1 + 1 \cdot \frac{1}{3 x}} \left|{3 x + 1}\right|$$
/ ___________\ d | / 1 | --||3*x + 1|*3 / 1*--- + 1 | dx\ \/ 3*x /
$$\frac{d}{d x} \sqrt[3]{1 + 1 \cdot \frac{1}{3 x}} \left|{3 x + 1}\right|$$
The first derivative
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___________
/ 1 |3*x + 1|
3*3 / 1*--- + 1 *sign(1 + 3*x) - -------------------
\/ 3*x 2/3
2 / 1 \
9*x *|1*--- + 1|
\ 3*x /
$$3 \sqrt[3]{1 + 1 \cdot \frac{1}{3 x}} \operatorname{sign}{\left(3 x + 1 \right)} - \frac{\left|{3 x + 1}\right|}{9 x^{2} \left(1 + 1 \cdot \frac{1}{3 x}\right)^{\frac{2}{3}}}$$
The second derivative
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/ / 1 \ \ | |3 - ---------|*|1 + 3*x|| | | / 1\| | | _________ | x*|3 + -|| | | / 1 sign(1 + 3*x) \ \ x// | 2*|9*3 / 1 + --- *DiracDelta(1 + 3*x) - ----------------- + -------------------------| | \/ 3*x 2/3 2/3 | | 2 / 1 \ 3 / 1 \ | | 3*x *|1 + ---| 27*x *|1 + ---| | \ \ 3*x/ \ 3*x/ /
$$2 \cdot \left(9 \sqrt[3]{1 + \frac{1}{3 x}} \delta\left(3 x + 1\right) - \frac{\operatorname{sign}{\left(3 x + 1 \right)}}{3 x^{2} \left(1 + \frac{1}{3 x}\right)^{\frac{2}{3}}} + \frac{\left(3 - \frac{1}{x \left(3 + \frac{1}{x}\right)}\right) \left|{3 x + 1}\right|}{27 x^{3} \left(1 + \frac{1}{3 x}\right)^{\frac{2}{3}}}\right)$$
The third derivative
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/ / 18 5 \ \ | |27 - --------- + -----------|*|1 + 3*x| / 1 \ | | | / 1\ 2| |3 - ---------|*sign(1 + 3*x)| | | x*|3 + -| 2 / 1\ | | / 1\| | | _________ | \ x/ x *|3 + -| | | x*|3 + -|| | | / 1 3*DiracDelta(1 + 3*x) \ \ x/ / \ \ x// | 2*|27*3 / 1 + --- *DiracDelta(1 + 3*x, 1) - --------------------- - ---------------------------------------- + -----------------------------| | \/ 3*x 2/3 2/3 2/3 | | 2 / 1 \ 4 / 1 \ 3 / 1 \ | | x *|1 + ---| 81*x *|1 + ---| 3*x *|1 + ---| | \ \ 3*x/ \ 3*x/ \ 3*x/ /
$$2 \cdot \left(27 \sqrt[3]{1 + \frac{1}{3 x}} \delta^{\left( 1 \right)}\left( 3 x + 1 \right) - \frac{3 \delta\left(3 x + 1\right)}{x^{2} \left(1 + \frac{1}{3 x}\right)^{\frac{2}{3}}} + \frac{\left(3 - \frac{1}{x \left(3 + \frac{1}{x}\right)}\right) \operatorname{sign}{\left(3 x + 1 \right)}}{3 x^{3} \left(1 + \frac{1}{3 x}\right)^{\frac{2}{3}}} - \frac{\left(27 - \frac{18}{x \left(3 + \frac{1}{x}\right)} + \frac{5}{x^{2} \left(3 + \frac{1}{x}\right)^{2}}\right) \left|{3 x + 1}\right|}{81 x^{4} \left(1 + \frac{1}{3 x}\right)^{\frac{2}{3}}}\right)$$