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- Derivative of:
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Derivative of sin(4x)
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Derivative of x^e
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Derivative of (x^3-1)(x^2+x+1)
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Derivative of log(x+2)
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Identical expressions
- arcctg(sqrt(x))/lnx+ one
- arcctg( square root of (x)) divide by lnx plus 1
- arcctg( square root of (x)) divide by lnx plus one
- arcctg(√(x))/lnx+1
- arcctgsqrtx/lnx+1
- arcctg(sqrt(x)) divide by lnx+1
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Similar expressions
- arcctg(sqrt(x))/lnx-1
Derivative of arcctg(sqrt(x))/lnx+1
The solution
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[src]
/ ___\ acot\\/ x / ----------- + 1 log(x)
$$1 + \frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{\log{\left(x \right)}}$$
acot(sqrt(x))/log(x) + 1
The first derivative
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/ ___\
acot\\/ x / 1
- ----------- - ----------------------
2 ___
x*log (x) 2*\/ x *(1 + x)*log(x)
$$- \frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{x \log{\left(x \right)}^{2}} - \frac{1}{2 \sqrt{x} \left(x + 1\right) \log{\left(x \right)}}$$
The second derivative
[src]
/ ___\ / ___\
1 1 acot\\/ x / 1 2*acot\\/ x /
---------------- + -------------- + ----------- + ------------------- + -------------
___ 2 3/2 2 3/2 2 2
2*\/ x *(1 + x) 4*x *(1 + x) x *log(x) x *(1 + x)*log(x) x *log (x)
-------------------------------------------------------------------------------------
log(x)
$$\frac{\frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{x^{2} \log{\left(x \right)}} + \frac{2 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{1}{2 \sqrt{x} \left(x + 1\right)^{2}} + \frac{1}{4 x^{\frac{3}{2}} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}} \left(x + 1\right) \log{\left(x \right)}}}{\log{\left(x \right)}}$$
The third derivative
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/ / ___\ / ___\ / ___\ \
| 1 1 3 2*acot\\/ x / 3 6*acot\\/ x / 6*acot\\/ x / 3 9 |
-|-------------- + --------------- + -------------- + ------------- + -------------------- + ------------- + ------------- + ---------------------- + ---------------------|
| ___ 3 3/2 2 5/2 3 5/2 2 3 3 3 2 3/2 2 5/2 |
\\/ x *(1 + x) 2*x *(1 + x) 8*x *(1 + x) x *log(x) x *(1 + x)*log (x) x *log (x) x *log (x) 2*x *(1 + x) *log(x) 4*x *(1 + x)*log(x)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x)
$$- \frac{\frac{2 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{3} \log{\left(x \right)}} + \frac{6 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{6 \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{3} \log{\left(x \right)}^{3}} + \frac{1}{\sqrt{x} \left(x + 1\right)^{3}} + \frac{1}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2} \log{\left(x \right)}} + \frac{3}{8 x^{\frac{5}{2}} \left(x + 1\right)} + \frac{9}{4 x^{\frac{5}{2}} \left(x + 1\right) \log{\left(x \right)}} + \frac{3}{x^{\frac{5}{2}} \left(x + 1\right) \log{\left(x \right)}^{2}}}{\log{\left(x \right)}}$$