Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of (x-1)/(x+1)
-
Derivative of 4x^2
-
Derivative of sqrt(x^3)
-
Derivative of sqrt(x^2)
-
Identical expressions
- arcsin(lnx^ four +arctgx^ two)+x^(one +x)
- arc sinus of (lnx to the power of 4 plus arctgx squared ) plus x to the power of (1 plus x)
- arc sinus of (lnx to the power of four plus arctgx to the power of two) plus x to the power of (one plus x)
- arcsin(lnx4+arctgx2)+x(1+x)
- arcsinlnx4+arctgx2+x1+x
- arcsin(lnx⁴+arctgx²)+x^(1+x)
- arcsin(lnx to the power of 4+arctgx to the power of 2)+x to the power of (1+x)
- arcsinlnx^4+arctgx^2+x^1+x
-
Similar expressions
- arcsin(lnx^4+arctgx^2)-x^(1+x)
- arcsin(lnx^4-arctgx^2)+x^(1+x)
- arcsin(lnx^4+arctgx^2)+x^(1-x)
Derivative of arcsin(lnx^4+arctgx^2)+x^(1+x)
The solution
You have entered
[src]
/ 4 2 \ 1 + x asin\log (x) + acot (x)/ + x
$$x^{x + 1} + \operatorname{asin}{\left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)} \right)}$$
asin(log(x)^4 + acot(x)^2) + x^(1 + x)
The first derivative
[src]
3
2*acot(x) 4*log (x)
- --------- + ---------
2 x
1 + x /1 + x \ 1 + x
x *|----- + log(x)| + -------------------------------
\ x / ___________________________
/ 2
/ / 4 2 \
\/ 1 - \log (x) + acot (x)/
$$x^{x + 1} \left(\log{\left(x \right)} + \frac{x + 1}{x}\right) + \frac{- \frac{2 \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{4 \log{\left(x \right)}^{3}}{x}}{\sqrt{1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}}}$$
The second derivative
[src]
/ 3 2 \ 2
| 1 2*log (x) 6*log (x) 2*x*acot(x)| / 3 \
2*|--------- - --------- + --------- + -----------| |acot(x) 2*log (x)| / 2 4 \
| 2 2 2 2 | 1 + x / 1 + x\ 4*|------- - ---------| *\acot (x) + log (x)/
2 |/ 2\ x x / 2\ | x *|2 - -----| | 2 x |
1 + x /1 + x \ \\1 + x / \1 + x / / \ x / \ 1 + x /
x *|----- + log(x)| + --------------------------------------------------- + ------------------ + ---------------------------------------------
\ x / ___________________________ x 3/2
/ 2 / 2\
/ / 2 4 \ | / 2 4 \ |
\/ 1 - \acot (x) + log (x)/ \1 - \acot (x) + log (x)/ /
$$x^{x + 1} \left(\log{\left(x \right)} + \frac{x + 1}{x}\right)^{2} + \frac{2 \left(\frac{2 x \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}^{3}}{x^{2}} + \frac{6 \log{\left(x \right)}^{2}}{x^{2}}\right)}{\sqrt{1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}}} + \frac{4 \left(\frac{\operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \frac{2 \log{\left(x \right)}^{3}}{x}\right)^{2} \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)}{\left(1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}\right)^{\frac{3}{2}}} + \frac{x^{x + 1} \left(2 - \frac{x + 1}{x}\right)}{x}$$
The third derivative
[src]
3 / 3 2 2 \ 3 / 3 \ / 3 2 \
/ 3 \ | acot(x) 6*log(x) 2*log (x) 3*x 9*log (x) 4*x *acot(x)| 2 / 3 \ / 2 4 \ |acot(x) 2*log (x)| | 1 2*log (x) 6*log (x) 2*x*acot(x)|
|acot(x) 2*log (x)| 4*|- --------- - -------- - --------- + --------- + --------- + ------------| / 2 4 \ |acot(x) 2*log (x)| 12*\acot (x) + log (x)/*|------- - ---------|*|--------- - --------- + --------- + -----------|
8*|------- - ---------| | 2 3 3 3 3 3 | 1 + x / 2*(1 + x)\ 24*\acot (x) + log (x)/ *|------- - ---------| | 2 x | | 2 2 2 2 | 1 + x / 1 + x\ /1 + x \
3 | 2 x | | / 2\ x x / 2\ x / 2\ | x *|3 - ---------| | 2 x | \ 1 + x / |/ 2\ x x / 2\ | 3*x *|2 - -----|*|----- + log(x)|
1 + x /1 + x \ \ 1 + x / \ \1 + x / \1 + x / \1 + x / / \ x / \ 1 + x / \\1 + x / \1 + x / / \ x / \ x /
x *|----- + log(x)| - ------------------------------ - ----------------------------------------------------------------------------- - ---------------------- - ----------------------------------------------- - ----------------------------------------------------------------------------------------------- + -------------------------------------
\ x / 3/2 ___________________________ 2 5/2 3/2 x
/ 2\ / 2 x / 2\ / 2\
| / 2 4 \ | / / 2 4 \ | / 2 4 \ | | / 2 4 \ |
\1 - \acot (x) + log (x)/ / \/ 1 - \acot (x) + log (x)/ \1 - \acot (x) + log (x)/ / \1 - \acot (x) + log (x)/ /
$$x^{x + 1} \left(\log{\left(x \right)} + \frac{x + 1}{x}\right)^{3} - \frac{4 \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{3 x}{\left(x^{2} + 1\right)^{3}} - \frac{\operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}^{3}}{x^{3}} + \frac{9 \log{\left(x \right)}^{2}}{x^{3}} - \frac{6 \log{\left(x \right)}}{x^{3}}\right)}{\sqrt{1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}}} - \frac{8 \left(\frac{\operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \frac{2 \log{\left(x \right)}^{3}}{x}\right)^{3}}{\left(1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}\right)^{\frac{3}{2}}} - \frac{12 \left(\frac{\operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \frac{2 \log{\left(x \right)}^{3}}{x}\right) \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right) \left(\frac{2 x \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}^{3}}{x^{2}} + \frac{6 \log{\left(x \right)}^{2}}{x^{2}}\right)}{\left(1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}\right)^{\frac{3}{2}}} - \frac{24 \left(\frac{\operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \frac{2 \log{\left(x \right)}^{3}}{x}\right)^{3} \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}}{\left(1 - \left(\log{\left(x \right)}^{4} + \operatorname{acot}^{2}{\left(x \right)}\right)^{2}\right)^{\frac{5}{2}}} + \frac{3 x^{x + 1} \left(2 - \frac{x + 1}{x}\right) \left(\log{\left(x \right)} + \frac{x + 1}{x}\right)}{x} - \frac{x^{x + 1} \left(3 - \frac{2 \left(x + 1\right)}{x}\right)}{x^{2}}$$