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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 cos(x^3)
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Derivative of (cos(x))^3
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Derivative of 1/tan(x)
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Derivative of (x^5+1)
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Identical expressions
- three *(x+ one)^ two *|x|^(two / three)+ two *(x+ one)^ three *|x|^(two / three)*x/ three
- 3 multiply by (x plus 1) squared multiply by module of x| to the power of (2 divide by 3) plus 2 multiply by (x plus 1) cubed multiply by |x| to the power of (2 divide by 3) multiply by x divide by 3
- three multiply by (x plus one) to the power of two multiply by module of x| to the power of (two divide by three) plus two multiply by (x plus one) to the power of three multiply by |x| to the power of (two divide by three) multiply by x divide by three
- 3*(x+1)2*|x|(2/3)+2*(x+1)3*|x|(2/3)*x/3
- 3*x+12*|x|2/3+2*x+13*|x|2/3*x/3
- 3*(x+1)²*|x|^(2/3)+2*(x+1)³*|x|^(2/3)*x/3
- 3*(x+1) to the power of 2*|x| to the power of (2/3)+2*(x+1) to the power of 3*|x| to the power of (2/3)*x/3
- 3(x+1)^2|x|^(2/3)+2(x+1)^3|x|^(2/3)x/3
- 3(x+1)2|x|(2/3)+2(x+1)3|x|(2/3)x/3
- 3x+12|x|2/3+2x+13|x|2/3x/3
- 3x+1^2|x|^2/3+2x+1^3|x|^2/3x/3
- 3*(x+1)^2*|x|^(2 divide by 3)+2*(x+1)^3*|x|^(2 divide by 3)*x divide by 3
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Similar expressions
- 3*(x+1)^2*|x|^(2/3)-2*(x+1)^3*|x|^(2/3)*x/3
- 3*(x+1)^2*|x|^(2/3)+2*(x-1)^3*|x|^(2/3)*x/3
- 3*(x-1)^2*|x|^(2/3)+2*(x+1)^3*|x|^(2/3)*x/3
Derivative of 3*(x+1)^2*|x|^(2/3)+2*(x+1)^3*|x|^(2/3)*x/3
The solution
You have entered
[src]
3 2/3
2 2/3 2*(x + 1) *|x| *x
3*(x + 1) *|x| + -------------------
3
$$\frac{x 2 \left(x + 1\right)^{3} \left|{x}\right|^{\frac{2}{3}}}{3} + 3 \left(x + 1\right)^{2} \left|{x}\right|^{\frac{2}{3}}$$
(3*(x + 1)^2)*|x|^(2/3) + (((2*(x + 1)^3)*|x|^(2/3))*x)/3
The first derivative
[src]
/ 3 \
| 2 2/3 4*(x + 1) *sign(x)|
x*|6*(x + 1) *|x| + ------------------|
| 3 _____ | 3 2/3 2
2/3 \ 3*\/ |x| / 2*(x + 1) *|x| 2*(x + 1) *sign(x)
|x| *(6 + 6*x) + ------------------------------------------ + ----------------- + ------------------
3 3 3 _____
\/ |x|
$$\frac{x \left(\frac{4 \left(x + 1\right)^{3} \operatorname{sign}{\left(x \right)}}{3 \sqrt[3]{\left|{x}\right|}} + 6 \left(x + 1\right)^{2} \left|{x}\right|^{\frac{2}{3}}\right)}{3} + \frac{2 \left(x + 1\right)^{3} \left|{x}\right|^{\frac{2}{3}}}{3} + \frac{2 \left(x + 1\right)^{2} \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \left(6 x + 6\right) \left|{x}\right|^{\frac{2}{3}}$$
The second derivative
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/ / 2 2 2 \ \ | | 2/3 (1 + x) *sign (x) 6*(1 + x) *DiracDelta(x) 18*(1 + x)*sign(x)| | | 2*x*(1 + x)*|27*|x| - ----------------- + ------------------------ + ------------------| | | 2 2 2 | 4/3 3 _____ 3 _____ | 3 | | 2/3 2 2/3 2*(1 + x) *DiracDelta(x) 4*(1 + x)*sign(x) (1 + x) *sign (x) \ |x| \/ |x| \/ |x| / 4*(1 + x) *sign(x)| 2*|3*|x| + 2*(1 + x) *|x| + ------------------------ + ----------------- - ----------------- + ------------------------------------------------------------------------------------------- + ------------------| | 3 _____ 3 _____ 4/3 27 3 _____ | \ \/ |x| \/ |x| 3*|x| 9*\/ |x| /
$$2 \left(\frac{2 x \left(x + 1\right) \left(\frac{6 \left(x + 1\right)^{2} \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} - \frac{\left(x + 1\right)^{2} \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{18 \left(x + 1\right) \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + 27 \left|{x}\right|^{\frac{2}{3}}\right)}{27} + \frac{4 \left(x + 1\right)^{3} \operatorname{sign}{\left(x \right)}}{9 \sqrt[3]{\left|{x}\right|}} + 2 \left(x + 1\right)^{2} \left|{x}\right|^{\frac{2}{3}} + \frac{2 \left(x + 1\right)^{2} \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} - \frac{\left(x + 1\right)^{2} \operatorname{sign}^{2}{\left(x \right)}}{3 \left|{x}\right|^{\frac{4}{3}}} + \frac{4 \left(x + 1\right) \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + 3 \left|{x}\right|^{\frac{2}{3}}\right)$$
The third derivative
[src]
/ / 2 2 3 3 3 2 3 \ \ | | 2/3 27*(1 + x) *sign (x) 4*(1 + x) *sign (x) 18*(1 + x) *DiracDelta(x, 1) 162*(1 + x) *DiracDelta(x) 162*(1 + x)*sign(x) 18*(1 + x) *DiracDelta(x)*sign(x)| | | x*|81*|x| - -------------------- + ------------------- + ---------------------------- + -------------------------- + ------------------- - ---------------------------------| | | | 4/3 7/3 3 _____ 3 _____ 3 _____ 4/3 | 2 2 2 3 2 3 2 3 2 | |3*sign(x) 2/3 \ |x| |x| \/ |x| \/ |x| \/ |x| |x| / (1 + x) *DiracDelta(x, 1) sign (x)*(1 + x) 2*(1 + x) *sign(x) 6*(1 + x)*DiracDelta(x) (1 + x) *sign (x) 2*(1 + x) *DiracDelta(x) 2*(1 + x) *sign (x) (1 + x) *DiracDelta(x)*sign(x)| 4*|--------- + 3*|x| *(1 + x) + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------- - ---------------- + ------------------ + ----------------------- - ----------------- + ------------------------ + ------------------- - ------------------------------| | 3 _____ 81 3 _____ 4/3 3 _____ 3 _____ 4/3 3 _____ 7/3 4/3 | \ \/ |x| \/ |x| |x| \/ |x| \/ |x| 9*|x| 3*\/ |x| 9*|x| |x| /
$$4 \left(\frac{x \left(\frac{18 \left(x + 1\right)^{3} \delta^{\left( 1 \right)}\left( x \right)}{\sqrt[3]{\left|{x}\right|}} - \frac{18 \left(x + 1\right)^{3} \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{4 \left(x + 1\right)^{3} \operatorname{sign}^{3}{\left(x \right)}}{\left|{x}\right|^{\frac{7}{3}}} + \frac{162 \left(x + 1\right)^{2} \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} - \frac{27 \left(x + 1\right)^{2} \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{162 \left(x + 1\right) \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + 81 \left|{x}\right|^{\frac{2}{3}}\right)}{81} + \frac{2 \left(x + 1\right)^{3} \delta\left(x\right)}{3 \sqrt[3]{\left|{x}\right|}} - \frac{\left(x + 1\right)^{3} \operatorname{sign}^{2}{\left(x \right)}}{9 \left|{x}\right|^{\frac{4}{3}}} + \frac{\left(x + 1\right)^{2} \delta^{\left( 1 \right)}\left( x \right)}{\sqrt[3]{\left|{x}\right|}} + \frac{2 \left(x + 1\right)^{2} \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} - \frac{\left(x + 1\right)^{2} \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{2 \left(x + 1\right)^{2} \operatorname{sign}^{3}{\left(x \right)}}{9 \left|{x}\right|^{\frac{7}{3}}} + 3 \left(x + 1\right) \left|{x}\right|^{\frac{2}{3}} + \frac{6 \left(x + 1\right) \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} - \frac{\left(x + 1\right) \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{3 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}}\right)$$