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How to use it?
- Derivative of:
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Derivative of sin(4x)
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Derivative of 4/x^3
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Derivative of x/(x-4)
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Derivative of |x-1|
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Identical expressions
- (sin(three *x)- three *x*e^x+ three *x^ two)/(arctg(x)-sin(x)-(x^ three)/ six)
- ( sinus of (3 multiply by x) minus 3 multiply by x multiply by e to the power of x plus 3 multiply by x squared ) divide by (arctg(x) minus sinus of (x) minus (x cubed ) divide by 6)
- ( sinus of (three multiply by x) minus three multiply by x multiply by e to the power of x plus three multiply by x to the power of two) divide by (arctg(x) minus sinus of (x) minus (x to the power of three) divide by six)
- (sin(3*x)-3*x*ex+3*x2)/(arctg(x)-sin(x)-(x3)/6)
- sin3*x-3*x*ex+3*x2/arctgx-sinx-x3/6
- (sin(3*x)-3*x*e^x+3*x²)/(arctg(x)-sin(x)-(x³)/6)
- (sin(3*x)-3*x*e to the power of x+3*x to the power of 2)/(arctg(x)-sin(x)-(x to the power of 3)/6)
- (sin(3x)-3xe^x+3x^2)/(arctg(x)-sin(x)-(x^3)/6)
- (sin(3x)-3xex+3x2)/(arctg(x)-sin(x)-(x3)/6)
- sin3x-3xex+3x2/arctgx-sinx-x3/6
- sin3x-3xe^x+3x^2/arctgx-sinx-x^3/6
- (sin(3*x)-3*x*e^x+3*x^2) divide by (arctg(x)-sin(x)-(x^3) divide by 6)
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Similar expressions
- (sin(3*x)-3*x*e^x+3*x^2)/(arctg(x)+sin(x)-(x^3)/6)
- (sin(3*x)+3*x*e^x+3*x^2)/(arctg(x)-sin(x)-(x^3)/6)
- (sin(3*x)-3*x*e^x-3*x^2)/(arctg(x)-sin(x)-(x^3)/6)
- (sin(3*x)-3*x*e^x+3*x^2)/(arctg(x)-sin(x)+(x^3)/6)
- (sin(3*x)-3*x*e^x+3*x^2)/(arctg(x)-sinx-(x^3)/6)
Derivative of (sin(3*x)-3*x*e^x+3*x^2)/(arctg(x)-sin(x)-(x^3)/6)
The solution
You have entered
[src]
x 2
sin(3*x) - 3*x*E + 3*x
------------------------
3
x
atan(x) - sin(x) - --
6
$$\frac{3 x^{2} + \left(- e^{x} 3 x + \sin{\left(3 x \right)}\right)}{- \frac{x^{3}}{6} + \left(- \sin{\left(x \right)} + \operatorname{atan}{\left(x \right)}\right)}$$
(sin(3*x) - 3*x*E^x + 3*x^2)/(atan(x) - sin(x) - x^3/6)
The first derivative
[src]
/ 2 \
/ x 2\ |x 1 |
\sin(3*x) - 3*x*E + 3*x /*|-- - ------ + cos(x)|
x x |2 2 |
- 3*e + 3*cos(3*x) + 6*x - 3*x*e \ 1 + x /
---------------------------------- + -------------------------------------------------
3 2
x / 3\
atan(x) - sin(x) - -- | x |
6 |atan(x) - sin(x) - --|
\ 6 /
$$\frac{\left(3 x^{2} + \left(- e^{x} 3 x + \sin{\left(3 x \right)}\right)\right) \left(\frac{x^{2}}{2} + \cos{\left(x \right)} - \frac{1}{x^{2} + 1}\right)}{\left(- \frac{x^{3}}{6} + \left(- \sin{\left(x \right)} + \operatorname{atan}{\left(x \right)}\right)\right)^{2}} + \frac{- 3 x e^{x} + 6 x - 3 e^{x} + 3 \cos{\left(3 x \right)}}{- \frac{x^{3}}{6} + \left(- \sin{\left(x \right)} + \operatorname{atan}{\left(x \right)}\right)}$$
The second derivative
[src]
/ / 2 \\
| | / 2 2 \ ||
| | 3*|x - ------ + 2*cos(x)| ||
| | | 2 | ||
| / 2 x \ | \ 1 + x / 2*x ||
| / 2 2 \ / x x\ 2*\3*x - 3*x*e + sin(3*x)/*|x - sin(x) - --------------------------- + ---------||
| 6*|x - ------ + 2*cos(x)|*\-cos(3*x) - 2*x + x*e + e / | 3 2||
| | 2 | | x - 6*atan(x) + 6*sin(x) / 2\ ||
| x x \ 1 + x / \ \1 + x / /|
18*|-2 + 2*e + 3*sin(3*x) + x*e - -------------------------------------------------------- + -----------------------------------------------------------------------------------|
| 3 3 |
\ x - 6*atan(x) + 6*sin(x) x - 6*atan(x) + 6*sin(x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
x - 6*atan(x) + 6*sin(x)
$$\frac{18 \left(x e^{x} - \frac{6 \left(x^{2} + 2 \cos{\left(x \right)} - \frac{2}{x^{2} + 1}\right) \left(x e^{x} - 2 x + e^{x} - \cos{\left(3 x \right)}\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} + \frac{2 \left(3 x^{2} - 3 x e^{x} + \sin{\left(3 x \right)}\right) \left(x + \frac{2 x}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(x^{2} + 2 \cos{\left(x \right)} - \frac{2}{x^{2} + 1}\right)^{2}}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} - \sin{\left(x \right)}\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} + 2 e^{x} + 3 \sin{\left(3 x \right)} - 2\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}}$$
The third derivative
[src]
/ / 2 \ / 3 / 2*x \ / 2 2 \ \\
| | / 2 2 \ | | / 2 2 \ 18*|x - sin(x) + ---------|*|x - ------ + 2*cos(x)| ||
| | 3*|x - ------ + 2*cos(x)| | | 27*|x - ------ + 2*cos(x)| | 2| | 2 | ||
| | | 2 | | | | 2 | 2 | / 2\ | \ 1 + x / ||
| | \ 1 + x / 2*x | / x x\ / 2 x \ | 2 \ 1 + x / 8*x \ \1 + x / / ||
| 18*|x - sin(x) - --------------------------- + ---------|*\-cos(3*x) - 2*x + x*e + e / / 2 2 \ / x x\ 2*\3*x - 3*x*e + sin(3*x)/*|-1 - --------- - ---------------------------- + --------- + ---------------------------------------------------- + cos(x)||
| | 3 2| 9*|x - ------ + 2*cos(x)|*\-2 + 2*e + 3*sin(3*x) + x*e / | 2 2 3 3 ||
| | x - 6*atan(x) + 6*sin(x) / 2\ | | 2 | | / 2\ / 3 \ / 2\ x - 6*atan(x) + 6*sin(x) ||
| x x \ \1 + x / / \ 1 + x / \ \1 + x / \x - 6*atan(x) + 6*sin(x)/ \1 + x / /|
18*|3*e + 9*cos(3*x) + x*e - --------------------------------------------------------------------------------------- - ---------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------|
| 3 3 3 |
\ x - 6*atan(x) + 6*sin(x) x - 6*atan(x) + 6*sin(x) x - 6*atan(x) + 6*sin(x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
x - 6*atan(x) + 6*sin(x)
$$\frac{18 \left(x e^{x} - \frac{9 \left(x^{2} + 2 \cos{\left(x \right)} - \frac{2}{x^{2} + 1}\right) \left(x e^{x} + 2 e^{x} + 3 \sin{\left(3 x \right)} - 2\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} - \frac{2 \left(3 x^{2} - 3 x e^{x} + \sin{\left(3 x \right)}\right) \left(\frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{18 \left(x + \frac{2 x}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)}\right) \left(x^{2} + 2 \cos{\left(x \right)} - \frac{2}{x^{2} + 1}\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} - \frac{27 \left(x^{2} + 2 \cos{\left(x \right)} - \frac{2}{x^{2} + 1}\right)^{3}}{\left(x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}\right)^{2}} + \cos{\left(x \right)} - 1 - \frac{2}{\left(x^{2} + 1\right)^{2}}\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} + 3 e^{x} + 9 \cos{\left(3 x \right)} - \frac{18 \left(x + \frac{2 x}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(x^{2} + 2 \cos{\left(x \right)} - \frac{2}{x^{2} + 1}\right)^{2}}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}} - \sin{\left(x \right)}\right) \left(x e^{x} - 2 x + e^{x} - \cos{\left(3 x \right)}\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}}\right)}{x^{3} + 6 \sin{\left(x \right)} - 6 \operatorname{atan}{\left(x \right)}}$$