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How to use it?
- Derivative of:
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Derivative of x^e
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Derivative of (5*x-4)*(2*x^4-7*x+1)
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Derivative of -3*x^3+2*x^2-x-5
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Derivative of x/5+5/x
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Identical expressions
- (arccos(5x))/(ln(four *x))
- (arc co sinus of e of (5x)) divide by (ln(4 multiply by x))
- (arc co sinus of e of (5x)) divide by (ln(four multiply by x))
- (arccos(5x))/(ln(4x))
- arccos5x/ln4x
- (arccos(5x)) divide by (ln(4*x))
Derivative of (arccos(5x))/(ln(4*x))
The solution
You have entered
[src]
acos(5*x) --------- log(4*x)
$$\frac{\operatorname{acos}{\left(5 x \right)}}{\log{\left(4 x \right)}}$$
d /acos(5*x)\ --|---------| dx\ log(4*x)/
$$\frac{d}{d x} \frac{\operatorname{acos}{\left(5 x \right)}}{\log{\left(4 x \right)}}$$
The first derivative
[src]
5 acos(5*x)
- ----------------------- - -----------
___________ 2
/ 2 x*log (4*x)
\/ 1 - 25*x *log(4*x)
$$- \frac{5}{\sqrt{1 - 25 x^{2}} \log{\left(4 x \right)}} - \frac{\operatorname{acos}{\left(5 x \right)}}{x \log{\left(4 x \right)}^{2}}$$
The second derivative
[src]
/ 2 \
|1 + --------|*acos(5*x)
125*x 10 \ log(4*x)/
- -------------- + ------------------------- + ------------------------
3/2 ___________ 2
/ 2\ / 2 x *log(4*x)
\1 - 25*x / x*\/ 1 - 25*x *log(4*x)
-----------------------------------------------------------------------
log(4*x)
$$\frac{- \frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{10}{x \sqrt{1 - 25 x^{2}} \log{\left(4 x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(4 x \right)}}\right) \operatorname{acos}{\left(5 x \right)}}{x^{2} \log{\left(4 x \right)}}}{\log{\left(4 x \right)}}$$
The third derivative
[src]
/ 2 \
| 75*x | / 3 3 \
125*|-1 + ----------| / 2 \ 2*|1 + -------- + ---------|*acos(5*x)
| 2| 15*|1 + --------| | log(4*x) 2 |
\ -1 + 25*x / 375 \ log(4*x)/ \ log (4*x)/
--------------------- + ----------------------- - -------------------------- - --------------------------------------
3/2 3/2 ___________ 3
/ 2\ / 2\ 2 / 2 x *log(4*x)
\1 - 25*x / \1 - 25*x / *log(4*x) x *\/ 1 - 25*x *log(4*x)
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log(4*x)
$$\frac{\frac{125 \cdot \left(\frac{75 x^{2}}{25 x^{2} - 1} - 1\right)}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{375}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \log{\left(4 x \right)}} - \frac{15 \cdot \left(1 + \frac{2}{\log{\left(4 x \right)}}\right)}{x^{2} \sqrt{1 - 25 x^{2}} \log{\left(4 x \right)}} - \frac{2 \cdot \left(1 + \frac{3}{\log{\left(4 x \right)}} + \frac{3}{\log{\left(4 x \right)}^{2}}\right) \operatorname{acos}{\left(5 x \right)}}{x^{3} \log{\left(4 x \right)}}}{\log{\left(4 x \right)}}$$
The graph