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How to use it?
- Derivative of:
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Derivative of x/5
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Derivative of x*2
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Derivative of (x^2-1)^2
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Derivative of 1/x^10
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Identical expressions
- five *sqrt((three *x- four)/(three *x+ four))*(acot(two *x+ five))
- 5 multiply by square root of ((3 multiply by x minus 4) divide by (3 multiply by x plus 4)) multiply by ( arcco tangent of gent of (2 multiply by x plus 5))
- five multiply by square root of ((three multiply by x minus four) divide by (three multiply by x plus four)) multiply by ( arcco tangent of gent of (two multiply by x plus five))
- 5*√((3*x-4)/(3*x+4))*(acot(2*x+5))
- 5sqrt((3x-4)/(3x+4))(acot(2x+5))
- 5sqrt3x-4/3x+4acot2x+5
- 5*sqrt((3*x-4) divide by (3*x+4))*(acot(2*x+5))
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Similar expressions
- 5*sqrt((3*x-4)/(3*x-4))*(acot(2*x+5))
- 5*sqrt((3*x+4)/(3*x+4))*(acot(2*x+5))
- 5*sqrt((3*x-4)/(3*x+4))*(acot(2*x-5))
- 5*sqrt((3*x-4)/(3*x+4))*(arccot(2*x+5))
Derivative of 5*sqrt((3*x-4)/(3*x+4))*(acot(2*x+5))
The solution
You have entered
[src]
_________
/ 3*x - 4
5* / ------- *acot(2*x + 5)
\/ 3*x + 4
$$5 \sqrt{\frac{3 x - 4}{3 x + 4}} \operatorname{acot}{\left(2 x + 5 \right)}$$
(5*sqrt((3*x - 4)/(3*x + 4)))*acot(2*x + 5)
The first derivative
[src]
_________
_________ / 3*x - 4 / 3 3*(3*x - 4) \
/ 3*x - 4 5* / ------- *(3*x + 4)*|----------- - ------------|*acot(2*x + 5)
10* / ------- \/ 3*x + 4 |2*(3*x + 4) 2|
\/ 3*x + 4 \ 2*(3*x + 4) /
- ---------------- + --------------------------------------------------------------------
2 3*x - 4
1 + (2*x + 5)
$$- \frac{10 \sqrt{\frac{3 x - 4}{3 x + 4}}}{\left(2 x + 5\right)^{2} + 1} + \frac{5 \sqrt{\frac{3 x - 4}{3 x + 4}} \left(3 x + 4\right) \left(- \frac{3 \left(3 x - 4\right)}{2 \left(3 x + 4\right)^{2}} + \frac{3}{2 \left(3 x + 4\right)}\right) \operatorname{acot}{\left(2 x + 5 \right)}}{3 x - 4}$$
The second derivative
[src]
/ / -4 + 3*x\ \
| | -1 + --------| |
| / -4 + 3*x\ / -4 + 3*x\ | 2 2 4 + 3*x | |
__________ | 6*|-1 + --------| 9*|-1 + --------|*|-------- + ------- + -------------|*acot(5 + 2*x)|
/ -4 + 3*x | 8*(5 + 2*x) \ 4 + 3*x / \ 4 + 3*x / \-4 + 3*x 4 + 3*x -4 + 3*x / |
5* / -------- *|----------------- + --------------------------- + --------------------------------------------------------------------|
\/ 4 + 3*x | 2 / 2\ 4*(-4 + 3*x) |
|/ 2\ \1 + (5 + 2*x) /*(-4 + 3*x) |
\\1 + (5 + 2*x) / /
$$5 \sqrt{\frac{3 x - 4}{3 x + 4}} \left(\frac{8 \left(2 x + 5\right)}{\left(\left(2 x + 5\right)^{2} + 1\right)^{2}} + \frac{9 \left(\frac{3 x - 4}{3 x + 4} - 1\right) \left(\frac{2}{3 x + 4} + \frac{\frac{3 x - 4}{3 x + 4} - 1}{3 x - 4} + \frac{2}{3 x - 4}\right) \operatorname{acot}{\left(2 x + 5 \right)}}{4 \left(3 x - 4\right)} + \frac{6 \left(\frac{3 x - 4}{3 x + 4} - 1\right)}{\left(3 x - 4\right) \left(\left(2 x + 5\right)^{2} + 1\right)}\right)$$
The third derivative
[src]
/ / 2 \ \
| | / -4 + 3*x\ / -4 + 3*x\ / -4 + 3*x\ | |
| / 2 \ / -4 + 3*x\ | |-1 + --------| 6*|-1 + --------| 6*|-1 + --------| | |
| | 4*(5 + 2*x) | | -1 + --------| / -4 + 3*x\ | 8 8 \ 4 + 3*x / \ 4 + 3*x / 8 \ 4 + 3*x / | |
|16*|-1 + --------------| / -4 + 3*x\ / -4 + 3*x\ | 2 2 4 + 3*x | 27*|-1 + --------|*|----------- + ---------- + ---------------- + ----------------- + -------------------- + --------------------|*acot(5 + 2*x)|
__________ | | 2| 36*|-1 + --------|*(5 + 2*x) 27*|-1 + --------|*|-------- + ------- + -------------| \ 4 + 3*x / | 2 2 2 2 (-4 + 3*x)*(4 + 3*x) (-4 + 3*x)*(4 + 3*x)| |
/ -4 + 3*x | \ 1 + (5 + 2*x) / \ 4 + 3*x / \ 4 + 3*x / \-4 + 3*x 4 + 3*x -4 + 3*x / \(-4 + 3*x) (4 + 3*x) (-4 + 3*x) (-4 + 3*x) / |
-5* / -------- *|------------------------ + ---------------------------- + ------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------|
\/ 4 + 3*x | 2 2 / 2\ 8*(-4 + 3*x) |
| / 2\ / 2\ 2*\1 + (5 + 2*x) /*(-4 + 3*x) |
\ \1 + (5 + 2*x) / \1 + (5 + 2*x) / *(-4 + 3*x) /
$$- 5 \sqrt{\frac{3 x - 4}{3 x + 4}} \left(\frac{36 \left(2 x + 5\right) \left(\frac{3 x - 4}{3 x + 4} - 1\right)}{\left(3 x - 4\right) \left(\left(2 x + 5\right)^{2} + 1\right)^{2}} + \frac{16 \left(\frac{4 \left(2 x + 5\right)^{2}}{\left(2 x + 5\right)^{2} + 1} - 1\right)}{\left(\left(2 x + 5\right)^{2} + 1\right)^{2}} + \frac{27 \left(\frac{3 x - 4}{3 x + 4} - 1\right) \left(\frac{8}{\left(3 x + 4\right)^{2}} + \frac{6 \left(\frac{3 x - 4}{3 x + 4} - 1\right)}{\left(3 x - 4\right) \left(3 x + 4\right)} + \frac{8}{\left(3 x - 4\right) \left(3 x + 4\right)} + \frac{\left(\frac{3 x - 4}{3 x + 4} - 1\right)^{2}}{\left(3 x - 4\right)^{2}} + \frac{6 \left(\frac{3 x - 4}{3 x + 4} - 1\right)}{\left(3 x - 4\right)^{2}} + \frac{8}{\left(3 x - 4\right)^{2}}\right) \operatorname{acot}{\left(2 x + 5 \right)}}{8 \left(3 x - 4\right)} + \frac{27 \left(\frac{3 x - 4}{3 x + 4} - 1\right) \left(\frac{2}{3 x + 4} + \frac{\frac{3 x - 4}{3 x + 4} - 1}{3 x - 4} + \frac{2}{3 x - 4}\right)}{2 \left(3 x - 4\right) \left(\left(2 x + 5\right)^{2} + 1\right)}\right)$$