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How to use it?
- Derivative of:
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Derivative of (x+5)/(x+1)
- Derivative of -x/2
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Derivative of sin(4x)
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Derivative of x*2^x
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Identical expressions
- (two -x)^((3x+ four)/(x- one))
- (2 minus x) to the power of ((3x plus 4) divide by (x minus 1))
- (two minus x) to the power of ((3x plus four) divide by (x minus one))
- (2-x)((3x+4)/(x-1))
- 2-x3x+4/x-1
- 2-x^3x+4/x-1
- (2-x)^((3x+4) divide by (x-1))
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Similar expressions
- (2-x)^((3x+4)/(x+1))
- (2-x)^((3x-4)/(x-1))
- (2+x)^((3x+4)/(x-1))
Derivative of (2-x)^((3x+4)/(x-1))
The solution
You have entered
[src]
3*x + 4
-------
x - 1
(2 - x)
$$\left(2 - x\right)^{\frac{3 x + 4}{x - 1}}$$
(2 - x)^((3*x + 4)/(x - 1))
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
[src]
3*x + 4
-------
x - 1 // 3 3*x + 4 \ 3*x + 4 \
(2 - x) *||----- - --------|*log(2 - x) - ---------------|
||x - 1 2| (2 - x)*(x - 1)|
\\ (x - 1) / /
$$\left(2 - x\right)^{\frac{3 x + 4}{x - 1}} \left(\left(\frac{3}{x - 1} - \frac{3 x + 4}{\left(x - 1\right)^{2}}\right) \log{\left(2 - x \right)} - \frac{3 x + 4}{\left(2 - x\right) \left(x - 1\right)}\right)$$
The second derivative
[src]
/ 2 \
4 + 3*x | /4 + 3*x / 4 + 3*x\ \ 4 + 3*x / 4 + 3*x\ |
------- | |------- + |3 - -------|*log(2 - x)| 3 - ------- 2*|3 - -------|*log(2 - x)|
-1 + x | 3 \ -2 + x \ -1 + x/ / -1 + x 4 + 3*x 4 + 3*x \ -1 + x/ |
(2 - x) *|------ + ------------------------------------- + ----------- - --------- - ----------------- - --------------------------|
|-2 + x -1 + x -2 + x 2 (-1 + x)*(-2 + x) -1 + x |
\ (-2 + x) /
------------------------------------------------------------------------------------------------------------------------------------------
-1 + x
$$\frac{\left(2 - x\right)^{\frac{3 x + 4}{x - 1}} \left(- \frac{2 \left(3 - \frac{3 x + 4}{x - 1}\right) \log{\left(2 - x \right)}}{x - 1} + \frac{3 - \frac{3 x + 4}{x - 1}}{x - 2} + \frac{\left(\left(3 - \frac{3 x + 4}{x - 1}\right) \log{\left(2 - x \right)} + \frac{3 x + 4}{x - 2}\right)^{2}}{x - 1} + \frac{3}{x - 2} - \frac{3 x + 4}{\left(x - 2\right) \left(x - 1\right)} - \frac{3 x + 4}{\left(x - 2\right)^{2}}\right)}{x - 1}$$
The third derivative
[src]
/ / 4 + 3*x / 4 + 3*x\ \ \
| | 3 - ------- 2*|3 - -------|*log(2 - x)| |
| 3 /4 + 3*x / 4 + 3*x\ \ | 3 4 + 3*x -1 + x 4 + 3*x \ -1 + x/ | |
4 + 3*x | /4 + 3*x / 4 + 3*x\ \ 4 + 3*x / 4 + 3*x\ 3*|------- + |3 - -------|*log(2 - x)|*|- ------ + --------- - ----------- + ----------------- + --------------------------| / 4 + 3*x\ |
------- | |------- + |3 - -------|*log(2 - x)| 3 - ------- 4*|3 - -------| \ -2 + x \ -1 + x/ / | -2 + x 2 -2 + x (-1 + x)*(-2 + x) -1 + x | 6*|3 - -------|*log(2 - x)|
-1 + x | 6 \ -2 + x \ -1 + x/ / -1 + x 6 2*(4 + 3*x) \ -1 + x/ \ (-2 + x) / 2*(4 + 3*x) 2*(4 + 3*x) \ -1 + x/ |
(2 - x) *|- --------- + ------------------------------------- - ----------- - ----------------- + ----------- - ----------------- - ---------------------------------------------------------------------------------------------------------------------------- + ------------------ + ------------------ + --------------------------|
| 2 2 2 (-1 + x)*(-2 + x) 3 (-1 + x)*(-2 + x) -1 + x 2 2 2 |
\ (-2 + x) (-1 + x) (-2 + x) (-2 + x) (-1 + x)*(-2 + x) (-1 + x) *(-2 + x) (-1 + x) /
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-1 + x
$$\frac{\left(2 - x\right)^{\frac{3 x + 4}{x - 1}} \left(\frac{6 \left(3 - \frac{3 x + 4}{x - 1}\right) \log{\left(2 - x \right)}}{\left(x - 1\right)^{2}} - \frac{4 \left(3 - \frac{3 x + 4}{x - 1}\right)}{\left(x - 2\right) \left(x - 1\right)} - \frac{3 - \frac{3 x + 4}{x - 1}}{\left(x - 2\right)^{2}} - \frac{3 \left(\left(3 - \frac{3 x + 4}{x - 1}\right) \log{\left(2 - x \right)} + \frac{3 x + 4}{x - 2}\right) \left(\frac{2 \left(3 - \frac{3 x + 4}{x - 1}\right) \log{\left(2 - x \right)}}{x - 1} - \frac{3 - \frac{3 x + 4}{x - 1}}{x - 2} - \frac{3}{x - 2} + \frac{3 x + 4}{\left(x - 2\right) \left(x - 1\right)} + \frac{3 x + 4}{\left(x - 2\right)^{2}}\right)}{x - 1} + \frac{\left(\left(3 - \frac{3 x + 4}{x - 1}\right) \log{\left(2 - x \right)} + \frac{3 x + 4}{x - 2}\right)^{3}}{\left(x - 1\right)^{2}} - \frac{6}{\left(x - 2\right) \left(x - 1\right)} + \frac{2 \left(3 x + 4\right)}{\left(x - 2\right) \left(x - 1\right)^{2}} - \frac{6}{\left(x - 2\right)^{2}} + \frac{2 \left(3 x + 4\right)}{\left(x - 2\right)^{2} \left(x - 1\right)} + \frac{2 \left(3 x + 4\right)}{\left(x - 2\right)^{3}}\right)}{x - 1}$$