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How to use it?
- Derivative of:
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Derivative of 2*x-x^2
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Derivative of 2^x*x^2
- Derivative of loga^x
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Derivative of cos(x)/(x+6)
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Identical expressions
- three (arctg(arcsin(4x)))
- 3(arctg(arc sinus of (4x)))
- three (arctg(arc sinus of (4x)))
- 3arctgarcsin4x
Derivative of 3(arctg(arcsin(4x)))
The solution
You have entered
[src]
3*atan(asin(4*x))
$$3 \operatorname{atan}{\left(\operatorname{asin}{\left(4 x \right)} \right)}$$
3*atan(asin(4*x))
The first derivative
[src]
12
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___________
/ 2 \ / 2
\1 + asin (4*x)/*\/ 1 - 16*x
$$\frac{12}{\sqrt{1 - 16 x^{2}} \left(\operatorname{asin}^{2}{\left(4 x \right)} + 1\right)}$$
The second derivative
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/ 2*x asin(4*x) \
96*|-------------- + -----------------------------|
| 3/2 / 2 \ / 2\|
|/ 2\ \1 + asin (4*x)/*\-1 + 16*x /|
\\1 - 16*x / /
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2
1 + asin (4*x)
$$\frac{96 \left(\frac{2 x}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{\operatorname{asin}{\left(4 x \right)}}{\left(16 x^{2} - 1\right) \left(\operatorname{asin}^{2}{\left(4 x \right)} + 1\right)}\right)}{\operatorname{asin}^{2}{\left(4 x \right)} + 1}$$
The third derivative
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/ 2 2 \
| 1 2 48*x 8*asin (4*x) 24*x*asin(4*x) |
192*|-------------- - ------------------------------- + -------------- + -------------------------------- - ------------------------------|
| 3/2 3/2 5/2 2 3/2 2|
|/ 2\ / 2 \ / 2\ / 2\ / 2 \ / 2\ / 2 \ / 2\ |
\\1 - 16*x / \1 + asin (4*x)/*\1 - 16*x / \1 - 16*x / \1 + asin (4*x)/ *\1 - 16*x / \1 + asin (4*x)/*\-1 + 16*x / /
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2
1 + asin (4*x)
$$\frac{192 \left(\frac{48 x^{2}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} - \frac{24 x \operatorname{asin}{\left(4 x \right)}}{\left(16 x^{2} - 1\right)^{2} \left(\operatorname{asin}^{2}{\left(4 x \right)} + 1\right)} + \frac{1}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}} \left(\operatorname{asin}^{2}{\left(4 x \right)} + 1\right)} + \frac{8 \operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}} \left(\operatorname{asin}^{2}{\left(4 x \right)} + 1\right)^{2}}\right)}{\operatorname{asin}^{2}{\left(4 x \right)} + 1}$$