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- Derivative of:
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Derivative of 8^x
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Derivative of x/3+3/x
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Derivative of 6^x
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Derivative of 1/(x+1)^2
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Identical expressions
- ((arctgx)^coshx)
- ((arctgx) to the power of hyperbolic co sinus of e of ine of x)
- ((arctgx)coshx)
- arctgxcoshx
- arctgx^coshx
Derivative of ((arctgx)^coshx)
The solution
You have entered
[src]
cosh(x) acot (x)
$$\operatorname{acot}^{\cosh{\left(x \right)}}{\left(x \right)}$$
acot(x)^cosh(x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
cosh(x) / cosh(x) \
acot (x)*|log(acot(x))*sinh(x) - ----------------|
| / 2\ |
\ \1 + x /*acot(x)/
$$\left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \sinh{\left(x \right)} - \frac{\cosh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \operatorname{acot}^{\cosh{\left(x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
cosh(x) |/ cosh(x) \ cosh(x) 2*sinh(x) 2*x*cosh(x) |
acot (x)*||log(acot(x))*sinh(x) - ----------------| + cosh(x)*log(acot(x)) - ------------------ - ---------------- + -----------------|
|| / 2\ | 2 / 2\ 2 |
|\ \1 + x /*acot(x)/ / 2\ 2 \1 + x /*acot(x) / 2\ |
\ \1 + x / *acot (x) \1 + x / *acot(x)/
$$\left(\frac{2 x \cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \sinh{\left(x \right)} - \frac{\cosh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)^{2} + \log{\left(\operatorname{acot}{\left(x \right)} \right)} \cosh{\left(x \right)} - \frac{2 \sinh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{\cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}}\right) \operatorname{acot}^{\cosh{\left(x \right)}}{\left(x \right)}$$
The third derivative
[src]
/ 3 2 \
cosh(x) |/ cosh(x) \ / cosh(x) \ / cosh(x) 2*sinh(x) 2*x*cosh(x) \ 3*cosh(x) 3*sinh(x) 2*cosh(x) 2*cosh(x) 8*x *cosh(x) 6*x*cosh(x) 6*x*sinh(x) |
acot (x)*||log(acot(x))*sinh(x) - ----------------| + log(acot(x))*sinh(x) + 3*|log(acot(x))*sinh(x) - ----------------|*|cosh(x)*log(acot(x)) - ------------------ - ---------------- + -----------------| - ---------------- - ------------------ - ------------------ + ----------------- - ----------------- + ------------------ + -----------------|
|| / 2\ | | / 2\ | | 2 / 2\ 2 | / 2\ 2 3 2 3 3 2 |
|\ \1 + x /*acot(x)/ \ \1 + x /*acot(x)/ | / 2\ 2 \1 + x /*acot(x) / 2\ | \1 + x /*acot(x) / 2\ 2 / 2\ 3 / 2\ / 2\ / 2\ 2 / 2\ |
\ \ \1 + x / *acot (x) \1 + x / *acot(x)/ \1 + x / *acot (x) \1 + x / *acot (x) \1 + x / *acot(x) \1 + x / *acot(x) \1 + x / *acot (x) \1 + x / *acot(x)/
$$\left(- \frac{8 x^{2} \cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}{\left(x \right)}} + \frac{6 x \sinh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{6 x \cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}^{2}{\left(x \right)}} + \left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \sinh{\left(x \right)} - \frac{\cosh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)^{3} + 3 \left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \sinh{\left(x \right)} - \frac{\cosh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \left(\frac{2 x \cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \log{\left(\operatorname{acot}{\left(x \right)} \right)} \cosh{\left(x \right)} - \frac{2 \sinh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{\cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}}\right) + \log{\left(\operatorname{acot}{\left(x \right)} \right)} \sinh{\left(x \right)} - \frac{3 \cosh{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{3 \sinh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} + \frac{2 \cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{2 \cosh{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}^{3}{\left(x \right)}}\right) \operatorname{acot}^{\cosh{\left(x \right)}}{\left(x \right)}$$