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How to use it?
- Derivative of:
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Derivative of y=arctan(sinhx)
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Derivative of y=sin3xcosx
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Derivative of f(x)=4x²-5x³+9x
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Derivative of 3e^-x
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Identical expressions
- y=arctan(sinhx)
- y equally arc tangent of ( hyperbolic sinus of e of x)
- y=arctansinhx
Derivative of y=arctan(sinhx)
The solution
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atan(sinh(x))
$$\operatorname{atan}{\left(\sinh{\left(x \right)} \right)}$$
d --(atan(sinh(x))) dx
$$\frac{d}{d x} \operatorname{atan}{\left(\sinh{\left(x \right)} \right)}$$
The first derivative
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cosh(x)
------------
2
1 + sinh (x)
$$\frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The second derivative
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/ 2 \
| 2*cosh (x) |
|1 - ------------|*sinh(x)
| 2 |
\ 1 + sinh (x)/
--------------------------
2
1 + sinh (x)
$$\frac{\left(- \frac{2 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} + 1\right) \sinh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The third derivative
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/ 2 2 2 2 \
| 6*sinh (x) 2*cosh (x) 8*cosh (x)*sinh (x)|
|1 - ------------ - ------------ + -------------------|*cosh(x)
| 2 2 2 |
| 1 + sinh (x) 1 + sinh (x) / 2 \ |
\ \1 + sinh (x)/ /
---------------------------------------------------------------
2
1 + sinh (x)
$$\frac{\left(\frac{8 \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} - \frac{6 \sinh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} - \frac{2 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} + 1\right) \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The graph