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How to use it?
- Derivative of:
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Derivative of sin(x)/cos(x)
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Derivative of cos(x)^(3)
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Derivative of tan(x^3)
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Derivative of 1/(2*sqrt(x))
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Identical expressions
- ln(x)/(one +x)+arcsinx/ two
- ln(x) divide by (1 plus x) plus arc sinus of x divide by 2
- ln(x) divide by (one plus x) plus arc sinus of x divide by two
- lnx/1+x+arcsinx/2
- ln(x) divide by (1+x)+arcsinx divide by 2
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Similar expressions
- ln(x)/(1+x)-arcsinx/2
- ln(x)/(1-x)+arcsinx/2
Derivative of ln(x)/(1+x)+arcsinx/2
The solution
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[src]
log(x) asin(x) ------ + ------- 1 + x 2
$$\frac{\operatorname{asin}{\left(x \right)}}{2} + \frac{\log{\left(x \right)}}{x + 1}$$
log(x)/(1 + x) + asin(x)/2
The first derivative
[src]
1 1 log(x)
------------- + --------- - --------
________ x*(1 + x) 2
/ 2 (1 + x)
2*\/ 1 - x
$$- \frac{\log{\left(x \right)}}{\left(x + 1\right)^{2}} + \frac{1}{2 \sqrt{1 - x^{2}}} + \frac{1}{x \left(x + 1\right)}$$
The second derivative
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x 1 2 2*log(x)
------------- - ---------- - ---------- + --------
3/2 2 2 3
/ 2\ x *(1 + x) x*(1 + x) (1 + x)
2*\1 - x /
$$\frac{x}{2 \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \log{\left(x \right)}}{\left(x + 1\right)^{3}} - \frac{2}{x \left(x + 1\right)^{2}} - \frac{1}{x^{2} \left(x + 1\right)}$$
The third derivative
[src]
2
1 6*log(x) 2 3 6 3*x
------------- - -------- + ---------- + ----------- + ---------- + -------------
3/2 4 3 2 2 3 5/2
/ 2\ (1 + x) x *(1 + x) x *(1 + x) x*(1 + x) / 2\
2*\1 - x / 2*\1 - x /
$$\frac{3 x^{2}}{2 \left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 \log{\left(x \right)}}{\left(x + 1\right)^{4}} + \frac{1}{2 \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{x \left(x + 1\right)^{3}} + \frac{3}{x^{2} \left(x + 1\right)^{2}} + \frac{2}{x^{3} \left(x + 1\right)}$$