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How to use it?
- Derivative of:
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Derivative of tan(4*x-5)
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Derivative of sqrt(x)*x
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Derivative of sin(x)^(23)
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Derivative of arcsin(1/x)
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Identical expressions
- (one -tg(one /x))*(x^ two - one)^(one / two)-arccos(three *x)/(three *x+ two)^(one / three)
- (1 minus tg(1 divide by x)) multiply by (x squared minus 1) to the power of (1 divide by 2) minus arc co sinus of e of (3 multiply by x) divide by (3 multiply by x plus 2) to the power of (1 divide by 3)
- (one minus tg(one divide by x)) multiply by (x to the power of two minus one) to the power of (one divide by two) minus arc co sinus of e of (three multiply by x) divide by (three multiply by x plus two) to the power of (one divide by three)
- (1-tg(1/x))*(x2-1)(1/2)-arccos(3*x)/(3*x+2)(1/3)
- 1-tg1/x*x2-11/2-arccos3*x/3*x+21/3
- (1-tg(1/x))*(x²-1)^(1/2)-arccos(3*x)/(3*x+2)^(1/3)
- (1-tg(1/x))*(x to the power of 2-1) to the power of (1/2)-arccos(3*x)/(3*x+2) to the power of (1/3)
- (1-tg(1/x))(x^2-1)^(1/2)-arccos(3x)/(3x+2)^(1/3)
- (1-tg(1/x))(x2-1)(1/2)-arccos(3x)/(3x+2)(1/3)
- 1-tg1/xx2-11/2-arccos3x/3x+21/3
- 1-tg1/xx^2-1^1/2-arccos3x/3x+2^1/3
- (1-tg(1 divide by x))*(x^2-1)^(1 divide by 2)-arccos(3*x) divide by (3*x+2)^(1 divide by 3)
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Similar expressions
- (1-tg(1/x))*(x^2-1)^(1/2)-arccos(3*x)/(3*x-2)^(1/3)
- (1+tg(1/x))*(x^2-1)^(1/2)-arccos(3*x)/(3*x+2)^(1/3)
- (1-tg(1/x))*(x^2-1)^(1/2)+arccos(3*x)/(3*x+2)^(1/3)
- (1-tg(1/x))*(x^2+1)^(1/2)-arccos(3*x)/(3*x+2)^(1/3)
Derivative of (1-tg(1/x))*(x^2-1)^(1/2)-arccos(3*x)/(3*x+2)^(1/3)
The solution
You have entered
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________
/ /1\\ / 2 acos(3*x)
|1 - tan|-||*\/ x - 1 - -----------
\ \x// 3 _________
\/ 3*x + 2
$$\left(1 - \tan{\left(\frac{1}{x} \right)}\right) \sqrt{x^{2} - 1} - \frac{\operatorname{acos}{\left(3 x \right)}}{\sqrt[3]{3 x + 2}}$$
(1 - tan(1/x))*sqrt(x^2 - 1) - acos(3*x)/(3*x + 2)^(1/3)
The first derivative
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________
/ /1\\ / 2 / 2/1\\
x*|1 - tan|-|| \/ x - 1 *|1 + tan |-||
acos(3*x) 3 \ \x// \ \x//
------------ + ------------------------- + -------------- + -------------------------
4/3 __________ ________ 2
(3*x + 2) / 2 3 _________ / 2 x
\/ 1 - 9*x *\/ 3*x + 2 \/ x - 1
$$\frac{x \left(1 - \tan{\left(\frac{1}{x} \right)}\right)}{\sqrt{x^{2} - 1}} + \frac{\operatorname{acos}{\left(3 x \right)}}{\left(3 x + 2\right)^{\frac{4}{3}}} + \frac{3}{\sqrt{1 - 9 x^{2}} \sqrt[3]{3 x + 2}} + \frac{\sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}}$$
The second derivative
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_________ _________
/1\ 2 / /1\\ / 2 / 2/1\\ / 2/1\\ / 2 / 2/1\\ /1\
-1 + tan|-| x *|-1 + tan|-|| 2*\/ -1 + x *|1 + tan |-|| 2*|1 + tan |-|| 2*\/ -1 + x *|1 + tan |-||*tan|-|
\x/ 6 4*acos(3*x) \ \x// \ \x// \ \x// 27*x \ \x// \x/
- ------------ - -------------------------- - ------------ + ---------------- - ---------------------------- + --------------- + ------------------------- - -----------------------------------
_________ __________ 7/3 3/2 3 _________ 3/2 4
/ 2 / 2 4/3 (2 + 3*x) / 2\ x / 2 / 2\ 3 _________ x
\/ -1 + x \/ 1 - 9*x *(2 + 3*x) \-1 + x / x*\/ -1 + x \1 - 9*x / *\/ 2 + 3*x
$$\frac{x^{2} \left(\tan{\left(\frac{1}{x} \right)} - 1\right)}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \sqrt[3]{3 x + 2}} - \frac{\tan{\left(\frac{1}{x} \right)} - 1}{\sqrt{x^{2} - 1}} - \frac{4 \operatorname{acos}{\left(3 x \right)}}{\left(3 x + 2\right)^{\frac{7}{3}}} - \frac{6}{\sqrt{1 - 9 x^{2}} \left(3 x + 2\right)^{\frac{4}{3}}} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x \sqrt{x^{2} - 1}} - \frac{2 \sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{3}} - \frac{2 \sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \tan{\left(\frac{1}{x} \right)}}{x^{4}}$$
The third derivative
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2 _________ _________ _________ _________
/ 2/1\\ / 2/1\\ 3 / /1\\ / 2/1\\ / 2 / /1\\ / 2 / 2/1\\ / 2/1\\ /1\ / 2 2/1\ / 2/1\\ / 2 / 2/1\\ /1\
3*|1 + tan |-|| 3*|1 + tan |-|| 3*x *|-1 + tan|-|| 2*|1 + tan |-|| *\/ -1 + x 3*x*|-1 + tan|-|| 6*\/ -1 + x *|1 + tan |-|| 2 6*|1 + tan |-||*tan|-| 4*\/ -1 + x *tan |-|*|1 + tan |-|| 12*\/ -1 + x *|1 + tan |-||*tan|-|
\ \x// 27 28*acos(3*x) 36 81*x \ \x// \ \x// \ \x// \ \x// \ \x// 729*x \ \x// \x/ \x/ \ \x// \ \x// \x/
- --------------- + ------------------------- + ------------- + -------------------------- - -------------------------- - --------------- - ------------------ + ----------------------------- + ----------------- + ---------------------------- + ------------------------- - ---------------------- + ------------------------------------ + ------------------------------------
3/2 3/2 10/3 __________ 3/2 _________ 5/2 6 3/2 4 5/2 _________ 6 5
/ 2\ / 2\ 3 _________ (2 + 3*x) / 2 7/3 / 2\ 4/3 2 / 2 / 2\ x / 2\ x / 2\ 3 _________ 3 / 2 x x
\-1 + x / \1 - 9*x / *\/ 2 + 3*x \/ 1 - 9*x *(2 + 3*x) \1 - 9*x / *(2 + 3*x) x *\/ -1 + x \-1 + x / \-1 + x / \1 - 9*x / *\/ 2 + 3*x x *\/ -1 + x
$$- \frac{3 x^{3} \left(\tan{\left(\frac{1}{x} \right)} - 1\right)}{\left(x^{2} - 1\right)^{\frac{5}{2}}} + \frac{729 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}} \sqrt[3]{3 x + 2}} + \frac{3 x \left(\tan{\left(\frac{1}{x} \right)} - 1\right)}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{81 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(3 x + 2\right)^{\frac{4}{3}}} - \frac{3 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{28 \operatorname{acos}{\left(3 x \right)}}{\left(3 x + 2\right)^{\frac{10}{3}}} + \frac{36}{\sqrt{1 - 9 x^{2}} \left(3 x + 2\right)^{\frac{7}{3}}} + \frac{27}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \sqrt[3]{3 x + 2}} - \frac{3 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2} \sqrt{x^{2} - 1}} - \frac{6 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \tan{\left(\frac{1}{x} \right)}}{x^{3} \sqrt{x^{2} - 1}} + \frac{6 \sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{4}} + \frac{12 \sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \tan{\left(\frac{1}{x} \right)}}{x^{5}} + \frac{2 \sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)^{2}}{x^{6}} + \frac{4 \sqrt{x^{2} - 1} \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \tan^{2}{\left(\frac{1}{x} \right)}}{x^{6}}$$