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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of y=cos9x
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Derivative of log((x+1)/(x-1))
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Derivative of 8*sin(t)^(3)
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Derivative of (1-sin(2*x))/(1+cos(2*x))
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Identical expressions
- (2arcsinx)/(5x+3lnx/ln4)
- (2arc sinus of x) divide by (5x plus 3lnx divide by ln4)
- 2arcsinx/5x+3lnx/ln4
- (2arcsinx) divide by (5x+3lnx divide by ln4)
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Similar expressions
- (2arcsinx)/(5x-3lnx/ln4)
Derivative of (2arcsinx)/(5x+3lnx/ln4)
The solution
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[src]
2*asin(x)
--------------
3*log(x)
5*x + --------
log(4)
$$\frac{2 \operatorname{asin}{\left(x \right)}}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}}$$
(2*asin(x))/(5*x + (3*log(x))/log(4))
The first derivative
[src]
/ 3 \
2*|-5 - --------|*asin(x)
2 \ x*log(4)/
---------------------------- + -------------------------
________ 2
/ 2 / 3*log(x)\ / 3*log(x)\
\/ 1 - x *|5*x + --------| |5*x + --------|
\ log(4) / \ log(4) /
$$\frac{2 \left(-5 - \frac{3}{x \log{\left(4 \right)}}\right) \operatorname{asin}{\left(x \right)}}{\left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right)^{2}} + \frac{2}{\sqrt{1 - x^{2}} \left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right)}$$
The second derivative
[src]
/ / 2 \ \
| | / 3 \ | |
| |2*|5 + --------| | |
| | \ x*log(4)/ 3 | |
| |----------------- + ---------|*asin(x) |
| | 3*log(x) 2 | / 3 \ |
| | 5*x + -------- x *log(4)| 2*|5 + --------| |
| x \ log(4) / \ x*log(4)/ |
2*|----------- + --------------------------------------- - ----------------------------|
| 3/2 3*log(x) ________ |
|/ 2\ 5*x + -------- / 2 / 3*log(x)\|
|\1 - x / log(4) \/ 1 - x *|5*x + --------||
\ \ log(4) //
----------------------------------------------------------------------------------------
3*log(x)
5*x + --------
log(4)
$$\frac{2 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{2 \left(5 + \frac{3}{x \log{\left(4 \right)}}\right)^{2}}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}} + \frac{3}{x^{2} \log{\left(4 \right)}}\right) \operatorname{asin}{\left(x \right)}}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}} - \frac{2 \left(5 + \frac{3}{x \log{\left(4 \right)}}\right)}{\sqrt{1 - x^{2}} \left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right)}\right)}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}}$$
The third derivative
[src]
/ / 3 \ \
| | / 3 \ / 3 \ | / 2 \ |
| | |5 + --------| 3*|5 + --------| | | / 3 \ | |
| | 1 \ x*log(4)/ \ x*log(4)/ | |2*|5 + --------| | |
| 2 6*|--------- + ----------------- + --------------------------|*asin(x) | \ x*log(4)/ 3 | |
| 3*x | 3 2 2 / 3*log(x)\ | 3*|----------------- + ---------| |
| -1 + ------- |x *log(4) / 3*log(x)\ x *|5*x + --------|*log(4)| | 3*log(x) 2 | / 3 \ |
| 2 | |5*x + --------| \ log(4) / | | 5*x + -------- x *log(4)| 3*x*|5 + --------| |
| -1 + x \ \ log(4) / / \ log(4) / \ x*log(4)/ |
2*|- ------------ - ---------------------------------------------------------------------- + --------------------------------- - ----------------------------|
| 3/2 3*log(x) ________ 3/2 |
| / 2\ 5*x + -------- / 2 / 3*log(x)\ / 2\ / 3*log(x)\|
| \1 - x / log(4) \/ 1 - x *|5*x + --------| \1 - x / *|5*x + --------||
\ \ log(4) / \ log(4) //
--------------------------------------------------------------------------------------------------------------------------------------------------------------
3*log(x)
5*x + --------
log(4)
$$\frac{2 \left(- \frac{3 x \left(5 + \frac{3}{x \log{\left(4 \right)}}\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right)} - \frac{6 \left(\frac{\left(5 + \frac{3}{x \log{\left(4 \right)}}\right)^{3}}{\left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right)^{2}} + \frac{3 \left(5 + \frac{3}{x \log{\left(4 \right)}}\right)}{x^{2} \left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right) \log{\left(4 \right)}} + \frac{1}{x^{3} \log{\left(4 \right)}}\right) \operatorname{asin}{\left(x \right)}}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}} + \frac{3 \left(\frac{2 \left(5 + \frac{3}{x \log{\left(4 \right)}}\right)^{2}}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}} + \frac{3}{x^{2} \log{\left(4 \right)}}\right)}{\sqrt{1 - x^{2}} \left(5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}\right)} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{5 x + \frac{3 \log{\left(x \right)}}{\log{\left(4 \right)}}}$$