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- Derivative of:
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Derivative of (x+5)/(x+1)
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Derivative of x^(4/3)
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Derivative of x*2^x
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Derivative of (x^2)/36
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Identical expressions
- 5arcsin^ four (x- one)^ three
- 5arc sinus of to the power of 4(x minus 1) cubed
- 5arc sinus of to the power of four (x minus one) to the power of three
- 5arcsin4(x-1)3
- 5arcsin4x-13
- 5arcsin⁴(x-1)³
- 5arcsin to the power of 4(x-1) to the power of 3
- 5arcsin^4x-1^3
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Similar expressions
- 5arcsin^4(x+1)^3
Derivative of 5arcsin^4(x-1)^3
The solution
You have entered
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64 5*asin (x - 1)
$$5 \operatorname{asin}^{64}{\left(x - 1 \right)}$$
5*asin(x - 1)^64
The first derivative
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63 320*asin (x - 1) ----------------- ______________ / 2 \/ 1 - (x - 1)
$$\frac{320 \operatorname{asin}^{63}{\left(x - 1 \right)}}{\sqrt{1 - \left(x - 1\right)^{2}}}$$
The second derivative
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62 / 63 (-1 + x)*asin(-1 + x)\
-320*asin (-1 + x)*|-------------- - ---------------------|
| 2 3/2 |
|-1 + (-1 + x) / 2\ |
\ \1 - (-1 + x) / /
$$- 320 \left(\frac{63}{\left(x - 1\right)^{2} - 1} - \frac{\left(x - 1\right) \operatorname{asin}{\left(x - 1 \right)}}{\left(1 - \left(x - 1\right)^{2}\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{62}{\left(x - 1 \right)}$$
The third derivative
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/ 2 2 2 \
61 | 3906 asin (-1 + x) 3*(-1 + x) *asin (-1 + x) 189*(-1 + x)*asin(-1 + x)|
320*asin (-1 + x)*|------------------ + ------------------ + ------------------------- + -------------------------|
| 3/2 3/2 5/2 2 |
|/ 2\ / 2\ / 2\ / 2\ |
\\1 - (-1 + x) / \1 - (-1 + x) / \1 - (-1 + x) / \-1 + (-1 + x) / /
$$320 \left(\frac{189 \left(x - 1\right) \operatorname{asin}{\left(x - 1 \right)}}{\left(\left(x - 1\right)^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x - 1 \right)}}{\left(1 - \left(x - 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{3906}{\left(1 - \left(x - 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(x - 1\right)^{2} \operatorname{asin}^{2}{\left(x - 1 \right)}}{\left(1 - \left(x - 1\right)^{2}\right)^{\frac{5}{2}}}\right) \operatorname{asin}^{61}{\left(x - 1 \right)}$$