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- Derivative of:
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Identical expressions
- sh3x^arctg(x+ two)
- sh3x to the power of arctg(x plus 2)
- sh3x to the power of arctg(x plus two)
- sh3xarctg(x+2)
- sh3xarctgx+2
- sh3x^arctgx+2
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Similar expressions
- sh3x^arctg(x-2)
Derivative of sh3x^arctg(x+2)
The solution
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[src]
atan(x + 2) sinh (3*x)
$$\sinh^{\operatorname{atan}{\left(x + 2 \right)}}{\left(3 x \right)}$$
sinh(3*x)^atan(x + 2)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
[src]
atan(x + 2) /log(sinh(3*x)) 3*atan(x + 2)*cosh(3*x)\
sinh (3*x)*|-------------- + -----------------------|
| 2 sinh(3*x) |
\ 1 + (x + 2) /
$$\left(\frac{3 \cosh{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh{\left(3 x \right)}} + \frac{\log{\left(\sinh{\left(3 x \right)} \right)}}{\left(x + 2\right)^{2} + 1}\right) \sinh^{\operatorname{atan}{\left(x + 2 \right)}}{\left(3 x \right)}$$
The second derivative
[src]
/ 2 2 \
atan(2 + x) |/log(sinh(3*x)) 3*atan(2 + x)*cosh(3*x)\ 9*cosh (3*x)*atan(2 + x) 2*(2 + x)*log(sinh(3*x)) 6*cosh(3*x) |
sinh (3*x)*||-------------- + -----------------------| + 9*atan(2 + x) - ------------------------ - ------------------------ + ------------------------|
|| 2 sinh(3*x) | 2 2 / 2\ |
|\ 1 + (2 + x) / sinh (3*x) / 2\ \1 + (2 + x) /*sinh(3*x)|
\ \1 + (2 + x) / /
$$\left(- \frac{2 \left(x + 2\right) \log{\left(\sinh{\left(3 x \right)} \right)}}{\left(\left(x + 2\right)^{2} + 1\right)^{2}} + \left(\frac{3 \cosh{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh{\left(3 x \right)}} + \frac{\log{\left(\sinh{\left(3 x \right)} \right)}}{\left(x + 2\right)^{2} + 1}\right)^{2} + 9 \operatorname{atan}{\left(x + 2 \right)} - \frac{9 \cosh^{2}{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh^{2}{\left(3 x \right)}} + \frac{6 \cosh{\left(3 x \right)}}{\left(\left(x + 2\right)^{2} + 1\right) \sinh{\left(3 x \right)}}\right) \sinh^{\operatorname{atan}{\left(x + 2 \right)}}{\left(3 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 2 3 \
atan(2 + x) |/log(sinh(3*x)) 3*atan(2 + x)*cosh(3*x)\ 27 /log(sinh(3*x)) 3*atan(2 + x)*cosh(3*x)\ | 6*cosh(3*x) 2*(2 + x)*log(sinh(3*x)) 9*cosh (3*x)*atan(2 + x)| 2*log(sinh(3*x)) 54*atan(2 + x)*cosh(3*x) 27*cosh (3*x) 8*(2 + x) *log(sinh(3*x)) 54*cosh (3*x)*atan(2 + x) 18*(2 + x)*cosh(3*x) |
sinh (3*x)*||-------------- + -----------------------| + ------------ - 3*|-------------- + -----------------------|*|-9*atan(2 + x) - ------------------------ + ------------------------ + ------------------------| - ---------------- - ------------------------ - ------------------------- + ------------------------- + ------------------------- - -------------------------|
|| 2 sinh(3*x) | 2 | 2 sinh(3*x) | | / 2\ 2 2 | 2 sinh(3*x) / 2\ 2 3 3 2 |
|\ 1 + (2 + x) / 1 + (2 + x) \ 1 + (2 + x) / | \1 + (2 + x) /*sinh(3*x) / 2\ sinh (3*x) | / 2\ \1 + (2 + x) /*sinh (3*x) / 2\ sinh (3*x) / 2\ |
\ \ \1 + (2 + x) / / \1 + (2 + x) / \1 + (2 + x) / \1 + (2 + x) / *sinh(3*x)/
$$\left(\frac{8 \left(x + 2\right)^{2} \log{\left(\sinh{\left(3 x \right)} \right)}}{\left(\left(x + 2\right)^{2} + 1\right)^{3}} - \frac{18 \left(x + 2\right) \cosh{\left(3 x \right)}}{\left(\left(x + 2\right)^{2} + 1\right)^{2} \sinh{\left(3 x \right)}} + \left(\frac{3 \cosh{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh{\left(3 x \right)}} + \frac{\log{\left(\sinh{\left(3 x \right)} \right)}}{\left(x + 2\right)^{2} + 1}\right)^{3} - 3 \left(\frac{3 \cosh{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh{\left(3 x \right)}} + \frac{\log{\left(\sinh{\left(3 x \right)} \right)}}{\left(x + 2\right)^{2} + 1}\right) \left(\frac{2 \left(x + 2\right) \log{\left(\sinh{\left(3 x \right)} \right)}}{\left(\left(x + 2\right)^{2} + 1\right)^{2}} - 9 \operatorname{atan}{\left(x + 2 \right)} + \frac{9 \cosh^{2}{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh^{2}{\left(3 x \right)}} - \frac{6 \cosh{\left(3 x \right)}}{\left(\left(x + 2\right)^{2} + 1\right) \sinh{\left(3 x \right)}}\right) - \frac{54 \cosh{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh{\left(3 x \right)}} + \frac{54 \cosh^{3}{\left(3 x \right)} \operatorname{atan}{\left(x + 2 \right)}}{\sinh^{3}{\left(3 x \right)}} + \frac{27}{\left(x + 2\right)^{2} + 1} - \frac{27 \cosh^{2}{\left(3 x \right)}}{\left(\left(x + 2\right)^{2} + 1\right) \sinh^{2}{\left(3 x \right)}} - \frac{2 \log{\left(\sinh{\left(3 x \right)} \right)}}{\left(\left(x + 2\right)^{2} + 1\right)^{2}}\right) \sinh^{\operatorname{atan}{\left(x + 2 \right)}}{\left(3 x \right)}$$