Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of (x+1)/(x^2+1)
-
Derivative of (x^2)^(1/3)
-
Derivative of ln(x)^2
-
Derivative of ln(1+x)
-
Identical expressions
- sign(x^ three -x)*(lоg(x+ two))^(four / three)
- sign(x cubed minus x) multiply by (lоg(x plus 2)) to the power of (4 divide by 3)
- sign(x to the power of three minus x) multiply by (lоg(x plus two)) to the power of (four divide by three)
- sign(x3-x)*(lоg(x+2))(4/3)
- signx3-x*lоgx+24/3
- sign(x³-x)*(lоg(x+2))^(4/3)
- sign(x to the power of 3-x)*(lоg(x+2)) to the power of (4/3)
- sign(x^3-x)(lоg(x+2))^(4/3)
- sign(x3-x)(lоg(x+2))(4/3)
- signx3-xlоgx+24/3
- signx^3-xlоgx+2^4/3
- sign(x^3-x)*(lоg(x+2))^(4 divide by 3)
-
Similar expressions
- sign(x^3-x)*(lоg(x-2))^(4/3)
- sign(x^3+x)*(lоg(x+2))^(4/3)
Derivative of sign(x^3-x)*(lоg(x+2))^(4/3)
The solution
You have entered
[src]
/ 3 \ 4/3 sign\x - x/*log (x + 2)
$$\log{\left(x + 2 \right)}^{\frac{4}{3}} \operatorname{sign}{\left(x^{3} - x \right)}$$
sign(x^3 - x)*log(x + 2)^(4/3)
The first derivative
[src]
3 ____________ / 3 \
4/3 / 2\ / 3 \ 4*\/ log(x + 2) *sign\x - x/
log (x + 2)*\-2 + 6*x /*DiracDelta\x - x/ + -----------------------------
3*(x + 2)
$$\left(6 x^{2} - 2\right) \log{\left(x + 2 \right)}^{\frac{4}{3}} \delta\left(x^{3} - x\right) + \frac{4 \sqrt[3]{\log{\left(x + 2 \right)}} \operatorname{sign}{\left(x^{3} - x \right)}}{3 \left(x + 2\right)}$$
The second derivative
[src]
/ / 1 3 ____________\ / / 2\\ \ | 2*|- ------------- + 3*\/ log(2 + x) |*sign\x*\-1 + x // | | / 2 \ | 2/3 | 3 ____________ / 2\ / / 2\\| | 4/3 |/ 2\ / / 2\ \ / / 2\\| \ log (2 + x) / 8*\/ log(2 + x) *\-1 + 3*x /*DiracDelta\x*\-1 + x //| 2*|log (2 + x)*\\-1 + 3*x / *DiracDelta\x*\-1 + x /, 1/ + 6*x*DiracDelta\x*\-1 + x /// - -------------------------------------------------------- + ----------------------------------------------------| | 2 3*(2 + x) | \ 9*(2 + x) /
$$2 \left(\left(6 x \delta\left(x \left(x^{2} - 1\right)\right) + \left(3 x^{2} - 1\right)^{2} \delta^{\left( 1 \right)}\left( x \left(x^{2} - 1\right) \right)\right) \log{\left(x + 2 \right)}^{\frac{4}{3}} + \frac{8 \left(3 x^{2} - 1\right) \sqrt[3]{\log{\left(x + 2 \right)}} \delta\left(x \left(x^{2} - 1\right)\right)}{3 \left(x + 2\right)} - \frac{2 \left(3 \sqrt[3]{\log{\left(x + 2 \right)}} - \frac{1}{\log{\left(x + 2 \right)}^{\frac{2}{3}}}\right) \operatorname{sign}{\left(x \left(x^{2} - 1\right) \right)}}{9 \left(x + 2\right)^{2}}\right)$$
The third derivative
[src]
/ / 3 ____________ 2 9 \ / / 2\\ / 2\ / 1 3 ____________\ / / 2\\\ | / 2 \ 2*|- 18*\/ log(2 + x) + ------------- + -------------|*sign\x*\-1 + x // 4*\-1 + 3*x /*|- ------------- + 3*\/ log(2 + x) |*DiracDelta\x*\-1 + x //| | / 3 \ 3 ____________ |/ 2\ / / 2\ \ / / 2\\| | 5/3 2/3 | | 2/3 | | | 4/3 | / / 2\\ / 2\ / / 2\ \ / 2\ / / 2\ \| 4*\/ log(2 + x) *\\-1 + 3*x / *DiracDelta\x*\-1 + x /, 1/ + 6*x*DiracDelta\x*\-1 + x /// \ log (2 + x) log (2 + x)/ \ log (2 + x) / | 2*|log (2 + x)*\6*DiracDelta\x*\-1 + x // + \-1 + 3*x / *DiracDelta\x*\-1 + x /, 2/ + 18*x*\-1 + 3*x /*DiracDelta\x*\-1 + x /, 1// + ---------------------------------------------------------------------------------------- - ------------------------------------------------------------------------- - --------------------------------------------------------------------------| | 2 + x 3 2 | \ 27*(2 + x) 3*(2 + x) /
$$2 \left(\left(18 x \left(3 x^{2} - 1\right) \delta^{\left( 1 \right)}\left( x \left(x^{2} - 1\right) \right) + \left(3 x^{2} - 1\right)^{3} \delta^{\left( 2 \right)}\left( x \left(x^{2} - 1\right) \right) + 6 \delta\left(x \left(x^{2} - 1\right)\right)\right) \log{\left(x + 2 \right)}^{\frac{4}{3}} + \frac{4 \left(6 x \delta\left(x \left(x^{2} - 1\right)\right) + \left(3 x^{2} - 1\right)^{2} \delta^{\left( 1 \right)}\left( x \left(x^{2} - 1\right) \right)\right) \sqrt[3]{\log{\left(x + 2 \right)}}}{x + 2} - \frac{4 \left(3 x^{2} - 1\right) \left(3 \sqrt[3]{\log{\left(x + 2 \right)}} - \frac{1}{\log{\left(x + 2 \right)}^{\frac{2}{3}}}\right) \delta\left(x \left(x^{2} - 1\right)\right)}{3 \left(x + 2\right)^{2}} - \frac{2 \left(- 18 \sqrt[3]{\log{\left(x + 2 \right)}} + \frac{9}{\log{\left(x + 2 \right)}^{\frac{2}{3}}} + \frac{2}{\log{\left(x + 2 \right)}^{\frac{5}{3}}}\right) \operatorname{sign}{\left(x \left(x^{2} - 1\right) \right)}}{27 \left(x + 2\right)^{3}}\right)$$