Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of x^5*sin(x)
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Derivative of (x+5)*sqrt(x)
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Derivative of (x^2-x)/2
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Derivative of x^(-1/3)
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Identical expressions
- -e^asinh(x)
- minus e to the power of hyperbolic arc sinus of e of (x)
- -easinh(x)
- -easinhx
- -e^asinhx
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Similar expressions
- e^asinh(x)
Derivative of -e^asinh(x)
The solution
You have entered
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asinh(x) -e
$$- e^{\operatorname{asinh}{\left(x \right)}}$$
d / asinh(x)\ --\-e / dx
$$\frac{d}{d x} \left(- e^{\operatorname{asinh}{\left(x \right)}}\right)$$
The first derivative
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asinh(x) -e ----------- ________ / 2 \/ 1 + x
$$- \frac{e^{\operatorname{asinh}{\left(x \right)}}}{\sqrt{x^{2} + 1}}$$
The second derivative
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/ 1 x \ asinh(x) |- ------ + -----------|*e | 2 3/2| | 1 + x / 2\ | \ \1 + x / /
$$\left(- \frac{1}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right)^{\frac{3}{2}}}\right) e^{\operatorname{asinh}{\left(x \right)}}$$
The third derivative
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/ 1 x \ asinh(x)
-3*x*|- --------- + -----------|*e
| 2 5/2|
| / 2\ / 2\ |
\ \1 + x / \1 + x / /
$$- 3 x \left(- \frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{x}{\left(x^{2} + 1\right)^{\frac{5}{2}}}\right) e^{\operatorname{asinh}{\left(x \right)}}$$
The graph