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How to use it?
- Derivative of:
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Derivative of 1/3*x^3
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Derivative of x^(5/2)
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Derivative of (x-4)^2
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Derivative of x^3-3*x
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Identical expressions
- y=arctg(shx)+shxlnchx
- y equally arctg(shx) plus shxlnchx
- y=arctgshx+shxlnchx
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Similar expressions
- y=arctg(shx)-shxlnchx
- arctg(shx)+(shx)lnchx
Derivative of y=arctg(shx)+shxlnchx
The solution
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atan(sinh(x)) + sinh(x)*log(cosh(x))
$$\log{\left(\cosh{\left(x \right)} \right)} \sinh{\left(x \right)} + \operatorname{atan}{\left(\sinh{\left(x \right)} \right)}$$
atan(sinh(x)) + sinh(x)*log(cosh(x))
The first derivative
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2
cosh(x) sinh (x)
------------ + -------- + cosh(x)*log(cosh(x))
2 cosh(x)
1 + sinh (x)
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The second derivative
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/ 2 2 \ | 1 sinh (x) 2*cosh (x) | |3 + ------------ - -------- - --------------- + log(cosh(x))|*sinh(x) | 2 2 2 | | 1 + sinh (x) cosh (x) / 2 \ | \ \1 + sinh (x)/ /
$$\left(\log{\left(\cosh{\left(x \right)} \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + 3 + \frac{1}{\sinh^{2}{\left(x \right)} + 1} - \frac{2 \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}}\right) \sinh{\left(x \right)}$$
The third derivative
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3 2 4 2 3 2
cosh(x) 2*cosh (x) 2*sinh (x) 2*sinh (x) 6*sinh (x)*cosh(x) 8*cosh (x)*sinh (x)
3*cosh(x) + ------------ + cosh(x)*log(cosh(x)) - --------------- - ---------- + ---------- - ------------------ + -------------------
2 2 cosh(x) 3 2 3
1 + sinh (x) / 2 \ cosh (x) / 2 \ / 2 \
\1 + sinh (x)/ \1 + sinh (x)/ \1 + sinh (x)/
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{2 \sinh^{4}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} - \frac{2 \sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + 3 \cosh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} - \frac{6 \sinh^{2}{\left(x \right)} \cosh{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} - \frac{2 \cosh^{3}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} + \frac{8 \sinh^{2}{\left(x \right)} \cosh^{3}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{3}}$$