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How to use it?
- Derivative of:
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Derivative of cos(x/3)
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Derivative of √x
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Derivative of xcos(x)
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Derivative of x/(1+e^x)
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Identical expressions
- y=(five +sinx)arcsinx2
- y equally (5 plus sinus of x)arc sinus of x2
- y equally (five plus sinus of x)arc sinus of x2
- y=5+sinxarcsinx2
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Similar expressions
- y=(5-sinx)arcsinx2
Derivative of y=(5+sinx)arcsinx2
The solution
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(5 + sin(x))*asin(x)*2
$$2 \left(\sin{\left(x \right)} + 5\right) \operatorname{asin}{\left(x \right)}$$
((5 + sin(x))*asin(x))*2
The first derivative
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2*(5 + sin(x))
-------------- + 2*asin(x)*cos(x)
________
/ 2
\/ 1 - x
$$2 \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} + \frac{2 \left(\sin{\left(x \right)} + 5\right)}{\sqrt{1 - x^{2}}}$$
The second derivative
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/ 2*cos(x) x*(5 + sin(x))\ 2*|-asin(x)*sin(x) + ----------- + --------------| | ________ 3/2 | | / 2 / 2\ | \ \/ 1 - x \1 - x / /
$$2 \left(\frac{x \left(\sin{\left(x \right)} + 5\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{\sqrt{1 - x^{2}}}\right)$$
The third derivative
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/ / 2 \ \ | | 3*x | | | |-1 + -------|*(5 + sin(x)) | | | 2| | | 3*sin(x) \ -1 + x / 3*x*cos(x)| 2*|-asin(x)*cos(x) - ----------- - --------------------------- + -----------| | ________ 3/2 3/2| | / 2 / 2\ / 2\ | \ \/ 1 - x \1 - x / \1 - x / /
$$2 \left(\frac{3 x \cos{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \left(\sin{\left(x \right)} + 5\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$