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How to use it?
- Derivative of:
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Derivative of x^-6
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Derivative of (x+5)/(x+1)
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Derivative of x*2^x
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Derivative of e^sin(x)*cos(x)
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Identical expressions
- y=tg^32x*arcsinx^ five
- y equally tg cubed 2x multiply by arc sinus of x to the power of 5
- y equally tg cubed 2x multiply by arc sinus of x to the power of five
- y=tg32x*arcsinx5
- y=tg³2x*arcsinx⁵
- y=tg to the power of 32x*arcsinx to the power of 5
- y=tg^32xarcsinx^5
- y=tg32xarcsinx5
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Similar expressions
- y=tg^3*2x*arcsinx^5
Derivative of y=tg^32x*arcsinx^5
The solution
You have entered
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32 5 tan (x)*asin (x)
$$\tan^{32}{\left(x \right)} \operatorname{asin}^{5}{\left(x \right)}$$
tan(x)^32*asin(x)^5
The first derivative
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4 32
5 31 / 2 \ 5*asin (x)*tan (x)
asin (x)*tan (x)*\32 + 32*tan (x)/ + -------------------
________
/ 2
\/ 1 - x
$$\left(32 \tan^{2}{\left(x \right)} + 32\right) \tan^{31}{\left(x \right)} \operatorname{asin}^{5}{\left(x \right)} + \frac{5 \tan^{32}{\left(x \right)} \operatorname{asin}^{4}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
The second derivative
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/ / 2 \ \
3 30 | 2 / 4 x*asin(x) \ 2 / 2 \ / 2 \ 320*\1 + tan (x)/*asin(x)*tan(x)|
asin (x)*tan (x)*|5*tan (x)*|- ------- + -----------| + 32*asin (x)*\1 + tan (x)/*\31 + 33*tan (x)/ + --------------------------------|
| | 2 3/2| ________ |
| | -1 + x / 2\ | / 2 |
\ \ \1 - x / / \/ 1 - x /
$$\left(5 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{4}{x^{2} - 1}\right) \tan^{2}{\left(x \right)} + 32 \left(\tan^{2}{\left(x \right)} + 1\right) \left(33 \tan^{2}{\left(x \right)} + 31\right) \operatorname{asin}^{2}{\left(x \right)} + \frac{320 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \tan^{30}{\left(x \right)} \operatorname{asin}^{3}{\left(x \right)}$$
The third derivative
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/ / 2 2 2 \ / 2 \ 2 / 2 \ / 2 \ \
2 29 | 3 | 12 asin (x) 3*x *asin (x) 12*x*asin(x)| 3 / 2 \ | 4 / 2 \ 2 / 2 \| 2 / 2 \ / 4 x*asin(x) \ 480*asin (x)*\1 + tan (x)/*\31 + 33*tan (x)/*tan(x)|
asin (x)*tan (x)*|5*tan (x)*|----------- + ----------- + ------------- + ------------| + 64*asin (x)*\1 + tan (x)/*\2*tan (x) + 465*\1 + tan (x)/ + 94*tan (x)*\1 + tan (x)// + 480*tan (x)*\1 + tan (x)/*|- ------- + -----------|*asin(x) + ---------------------------------------------------|
| | 3/2 3/2 5/2 2 | | 2 3/2| ________ |
| |/ 2\ / 2\ / 2\ / 2\ | | -1 + x / 2\ | / 2 |
\ \\1 - x / \1 - x / \1 - x / \-1 + x / / \ \1 - x / / \/ 1 - x /
$$\left(480 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{4}{x^{2} - 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} \operatorname{asin}{\left(x \right)} + 64 \left(\tan^{2}{\left(x \right)} + 1\right) \left(465 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 94 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \tan^{4}{\left(x \right)}\right) \operatorname{asin}^{3}{\left(x \right)} + 5 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \tan^{3}{\left(x \right)} + \frac{480 \left(\tan^{2}{\left(x \right)} + 1\right) \left(33 \tan^{2}{\left(x \right)} + 31\right) \tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \tan^{29}{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}$$
The graph