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How to use it?
- Derivative of:
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Derivative of y=5x-6
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Derivative of x^6*e^x
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Derivative of x^5/5
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Derivative of x^5-5*x^3-20*x
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Identical expressions
- arctg(e^(3x)/(tsin2t))
- arctg(e to the power of (3x) divide by (t sinus of 2t))
- arctg(e(3x)/(tsin2t))
- arctge3x/tsin2t
- arctge^3x/tsin2t
- arctg(e^(3x) divide by (tsin2t))
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What you mean?
- atan(e^(3*x)/((tsin2*t)))
- atan(e^(3*x)*t/tsin2)
- atan(e^(3*x)*2*t/tsin)
- atan(e^(3*x)*in2*t/ts)
- atan(e*3*x/(tsin2*t))
- atan(e*3*x*t/tsin2)
- atan(e^(3*x)*in2*t/ts)
You entered:
arctg(e^(3x)/(tsin2t))
What you mean?
Derivative of arctg(e^(3x)/(tsin2t))
The solution
You have entered
[src]
/ 3*x \
| e |
atan|-------|
\tsin2*t/
$$\operatorname{atan}{\left(\frac{e^{3 x}}{t tsin_{2}} \right)}$$
/ / 3*x \\ d | | e || --|atan|-------|| dx\ \tsin2*t//
$$\frac{\partial}{\partial x} \operatorname{atan}{\left(\frac{e^{3 x}}{t tsin_{2}} \right)}$$
The first derivative
[src]
3*x
3*e
-----------------------
/ 6*x \
| e |
t*tsin2*|1 + ---------|
| 2 2|
\ t *tsin2 /
$$\frac{3 e^{3 x}}{t tsin_{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)}$$
The second derivative
[src]
/ 6*x \
| 2*e | 3*x
9*|1 - -------------------------|*e
| / 6*x \|
| 2 2 | e ||
| t *tsin2 *|1 + ---------||
| | 2 2||
\ \ t *tsin2 //
--------------------------------------
/ 6*x \
| e |
t*tsin2*|1 + ---------|
| 2 2|
\ t *tsin2 /
$$\frac{9 \cdot \left(- \frac{2 e^{6 x}}{t^{2} tsin_{2}^{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)} + 1\right) e^{3 x}}{t tsin_{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)}$$
The third derivative
[src]
/ 6*x 12*x \
| 8*e 8*e | 3*x
27*|1 - ------------------------- + --------------------------|*e
| / 6*x \ 2|
| 2 2 | e | / 6*x \ |
| t *tsin2 *|1 + ---------| 4 4 | e | |
| | 2 2| t *tsin2 *|1 + ---------| |
| \ t *tsin2 / | 2 2| |
\ \ t *tsin2 / /
--------------------------------------------------------------------
/ 6*x \
| e |
t*tsin2*|1 + ---------|
| 2 2|
\ t *tsin2 /
$$\frac{27 \cdot \left(\frac{8 e^{12 x}}{t^{4} tsin_{2}^{4} \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)^{2}} - \frac{8 e^{6 x}}{t^{2} tsin_{2}^{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)} + 1\right) e^{3 x}}{t tsin_{2} \cdot \left(\frac{e^{6 x}}{t^{2} tsin_{2}^{2}} + 1\right)}$$