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- Derivative of:
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Derivative of x^(4/5)
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Derivative of log(x^2+5)
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Derivative of e^(-2*x)
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Derivative of asin(2*x)
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Identical expressions
- arccos8x^ three
- arc co sinus of e of 8x cubed
- arc co sinus of e of 8x to the power of three
- arccos8x3
- arccos8x³
- arccos8x to the power of 3
Derivative of arccos8x^3
The solution
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[src]
3 acos (8*x)
$$\operatorname{acos}^{3}{\left(8 x \right)}$$
d / 3 \ --\acos (8*x)/ dx
$$\frac{d}{d x} \operatorname{acos}^{3}{\left(8 x \right)}$$
The first derivative
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2 -24*acos (8*x) -------------- ___________ / 2 \/ 1 - 64*x
$$- \frac{24 \operatorname{acos}^{2}{\left(8 x \right)}}{\sqrt{1 - 64 x^{2}}}$$
The second derivative
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/ 1 4*x*acos(8*x) \
-384*|---------- + --------------|*acos(8*x)
| 2 3/2|
|-1 + 64*x / 2\ |
\ \1 - 64*x / /
$$- 384 \cdot \left(\frac{4 x \operatorname{acos}{\left(8 x \right)}}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{64 x^{2} - 1}\right) \operatorname{acos}{\left(8 x \right)}$$
The third derivative
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/ 2 2 2 \
| 2 acos (8*x) 192*x *acos (8*x) 48*x*acos(8*x)|
1536*|- -------------- - -------------- - ----------------- + --------------|
| 3/2 3/2 5/2 2 |
| / 2\ / 2\ / 2\ / 2\ |
\ \1 - 64*x / \1 - 64*x / \1 - 64*x / \-1 + 64*x / /
$$1536 \left(- \frac{192 x^{2} \operatorname{acos}^{2}{\left(8 x \right)}}{\left(1 - 64 x^{2}\right)^{\frac{5}{2}}} + \frac{48 x \operatorname{acos}{\left(8 x \right)}}{\left(64 x^{2} - 1\right)^{2}} - \frac{\operatorname{acos}^{2}{\left(8 x \right)}}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}}\right)$$
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