Mister Exam
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How to use it?
- Derivative of:
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Derivative of x^2+3x
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Derivative of x^2-3*x+2
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Derivative of (x-2)^2*(x-4)+5
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Derivative of (x^2-1)*(x^4+2)
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Identical expressions
- y=(e^x^ two)arcsin3x
- y equally (e to the power of x squared )arc sinus of 3x
- y equally (e to the power of x to the power of two)arc sinus of 3x
- y=(ex2)arcsin3x
- y=ex2arcsin3x
- y=(e^x²)arcsin3x
- y=(e to the power of x to the power of 2)arcsin3x
- y=e^x^2arcsin3x
Derivative of y=(e^x^2)arcsin3x
The solution
You have entered
[src]
/ 2\ \x / e *asin(3*x)
$$e^{x^{2}} \operatorname{asin}{\left(3 x \right)}$$
/ / 2\ \ d | \x / | --\e *asin(3*x)/ dx
$$\frac{d}{d x} e^{x^{2}} \operatorname{asin}{\left(3 x \right)}$$
The first derivative
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/ 2\
\x / / 2\
3*e \x /
------------- + 2*x*asin(3*x)*e
__________
/ 2
\/ 1 - 9*x
$$2 x e^{x^{2}} \operatorname{asin}{\left(3 x \right)} + \frac{3 e^{x^{2}}}{\sqrt{1 - 9 x^{2}}}$$
The second derivative
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/ 2\ / / 2\ 12*x 27*x \ \x / |2*\1 + 2*x /*asin(3*x) + ------------- + -------------|*e | __________ 3/2| | / 2 / 2\ | \ \/ 1 - 9*x \1 - 9*x / /
$$\left(\frac{12 x}{\sqrt{1 - 9 x^{2}}} + \frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 2 \cdot \left(2 x^{2} + 1\right) \operatorname{asin}{\left(3 x \right)}\right) e^{x^{2}}$$
The third derivative
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/ / 2 \ \ | | 27*x | | | 27*|-1 + ---------| | | | 2| / 2\ 2 | / 2\ | \ -1 + 9*x / 18*\1 + 2*x / 162*x / 2\ | \x / |- ------------------- + ------------- + ------------- + 4*x*\3 + 2*x /*asin(3*x)|*e | 3/2 __________ 3/2 | | / 2\ / 2 / 2\ | \ \1 - 9*x / \/ 1 - 9*x \1 - 9*x / /
$$\left(\frac{162 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 4 x \left(2 x^{2} + 3\right) \operatorname{asin}{\left(3 x \right)} + \frac{18 \cdot \left(2 x^{2} + 1\right)}{\sqrt{1 - 9 x^{2}}} - \frac{27 \cdot \left(\frac{27 x^{2}}{9 x^{2} - 1} - 1\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) e^{x^{2}}$$
The graph