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- Derivative of:
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Derivative of sin(x)^2
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Derivative of y=cos9x
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Derivative of x^3-5x^2+x
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Derivative of log((x+1)/(x-1))
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Identical expressions
- ((3x+ two)/(3x- four))^(one -10x)
- ((3x plus 2) divide by (3x minus 4)) to the power of (1 minus 10x)
- ((3x plus two) divide by (3x minus four)) to the power of (one minus 10x)
- ((3x+2)/(3x-4))(1-10x)
- 3x+2/3x-41-10x
- 3x+2/3x-4^1-10x
- ((3x+2) divide by (3x-4))^(1-10x)
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Similar expressions
- ((3x+2)/(3x-4))^(1+10x)
- ((3x-2)/(3x-4))^(1-10x)
- ((3x+2)/(3x+4))^(1-10x)
Derivative of ((3x+2)/(3x-4))^(1-10x)
The solution
You have entered
[src]
1 - 10*x /3*x + 2\ |-------| \3*x - 4/
$$\left(\frac{3 x + 2}{3 x - 4}\right)^{1 - 10 x}$$
((3*x + 2)/(3*x - 4))^(1 - 10*x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
/ / 3 3*(3*x + 2)\\
| (1 - 10*x)*(3*x - 4)*|------- - -----------||
1 - 10*x | |3*x - 4 2||
/3*x + 2\ | /3*x + 2\ \ (3*x - 4) /|
|-------| *|- 10*log|-------| + --------------------------------------------|
\3*x - 4/ \ \3*x - 4/ 3*x + 2 /
$$\left(\frac{3 x + 2}{3 x - 4}\right)^{1 - 10 x} \left(\frac{\left(1 - 10 x\right) \left(3 x - 4\right) \left(\frac{3}{3 x - 4} - \frac{3 \left(3 x + 2\right)}{\left(3 x - 4\right)^{2}}\right)}{3 x + 2} - 10 \log{\left(\frac{3 x + 2}{3 x - 4} \right)}\right)$$
The second derivative
[src]
/ 2 \
|/ / 2 + 3*x \ \ / 2 + 3*x \ / 3*(-1 + 10*x) 3*(-1 + 10*x)\|
1 - 10*x || 3*|1 - --------|*(-1 + 10*x)| 3*|1 - --------|*|-20 + ------------- + -------------||
/2 + 3*x \ || /2 + 3*x \ \ -4 + 3*x/ | \ -4 + 3*x/ \ -4 + 3*x 2 + 3*x /|
|--------| *||10*log|--------| + ----------------------------| + ------------------------------------------------------|
\-4 + 3*x/ \\ \-4 + 3*x/ 2 + 3*x / 2 + 3*x /
$$\left(\frac{3 x + 2}{3 x - 4}\right)^{1 - 10 x} \left(\frac{3 \left(1 - \frac{3 x + 2}{3 x - 4}\right) \left(-20 + \frac{3 \left(10 x - 1\right)}{3 x + 2} + \frac{3 \left(10 x - 1\right)}{3 x - 4}\right)}{3 x + 2} + \left(\frac{3 \left(1 - \frac{3 x + 2}{3 x - 4}\right) \left(10 x - 1\right)}{3 x + 2} + 10 \log{\left(\frac{3 x + 2}{3 x - 4} \right)}\right)^{2}\right)$$
The third derivative
[src]
/ / / 2 + 3*x \ \ \
| 3 / 2 + 3*x \ / 5 5 -1 + 10*x -1 + 10*x -1 + 10*x \ | 3*|1 - --------|*(-1 + 10*x)| |
|/ / 2 + 3*x \ \ 54*|1 - --------|*|- -------- - ------- + ----------- + ---------- + --------------------| / 2 + 3*x \ | /2 + 3*x \ \ -4 + 3*x/ | / 3*(-1 + 10*x) 3*(-1 + 10*x)\|
1 - 10*x || 3*|1 - --------|*(-1 + 10*x)| \ -4 + 3*x/ | -4 + 3*x 2 + 3*x 2 2 (-4 + 3*x)*(2 + 3*x)| 9*|1 - --------|*|10*log|--------| + ----------------------------|*|-20 + ------------- + -------------||
/2 + 3*x \ || /2 + 3*x \ \ -4 + 3*x/ | \ (-4 + 3*x) (2 + 3*x) / \ -4 + 3*x/ \ \-4 + 3*x/ 2 + 3*x / \ -4 + 3*x 2 + 3*x /|
-|--------| *||10*log|--------| + ----------------------------| + ------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------|
\-4 + 3*x/ \\ \-4 + 3*x/ 2 + 3*x / 2 + 3*x 2 + 3*x /
$$- \left(\frac{3 x + 2}{3 x - 4}\right)^{1 - 10 x} \left(\frac{9 \left(1 - \frac{3 x + 2}{3 x - 4}\right) \left(\frac{3 \left(1 - \frac{3 x + 2}{3 x - 4}\right) \left(10 x - 1\right)}{3 x + 2} + 10 \log{\left(\frac{3 x + 2}{3 x - 4} \right)}\right) \left(-20 + \frac{3 \left(10 x - 1\right)}{3 x + 2} + \frac{3 \left(10 x - 1\right)}{3 x - 4}\right)}{3 x + 2} + \frac{54 \left(1 - \frac{3 x + 2}{3 x - 4}\right) \left(- \frac{5}{3 x + 2} + \frac{10 x - 1}{\left(3 x + 2\right)^{2}} - \frac{5}{3 x - 4} + \frac{10 x - 1}{\left(3 x - 4\right) \left(3 x + 2\right)} + \frac{10 x - 1}{\left(3 x - 4\right)^{2}}\right)}{3 x + 2} + \left(\frac{3 \left(1 - \frac{3 x + 2}{3 x - 4}\right) \left(10 x - 1\right)}{3 x + 2} + 10 \log{\left(\frac{3 x + 2}{3 x - 4} \right)}\right)^{3}\right)$$