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d/dx((tan^(-1)(x) (1+x))/(1-x)) = (x+1)/((1-x) (x^2+1))+((x+1) tan^(-1)(x))/(1-x)^2+(tan^(-1)(x))/(1-x)
Całe rozwiązanie
1)d/dx(((x+1) tan^(-1)(x))/(1-x))
2)(d/dx((x+1) tan^(-1)(x)))/(1-x)-((x+1) tan^(-1)(x) (d/dx(1-x)))/(1-x)^2
3) (d/dx((x+1) tan^(-1)(x)))/(1-x)-((x+1) tan^(-1)(x) (d/dx(1)-d/dx(x)))/(1-x)^2
4) -((x+1) tan^(-1)(x) (d/dx(1)))/(1-x)^2+((x+1) tan^(-1)(x) (d/dx(x)))/(1-x)^2+(tan^(-1)(x) (d/dx(x+1))+(x+1) (d/dx(tan^(-1)(x))))/(1-x)
5) ((x+1) tan^(-1)(x) (d/dx(x)))/(1-x)^2+(tan^(-1)(x) (d/dx(x+1)))/(1-x)+((x+1) (d/dx(tan^(-1)(x))))/(1-x)
6) (tan^(-1)(x) (d/dx(x+1)))/(1-x)+((x+1) (d/dx(tan^(-1)(x))))/(1-x)+((x+1) tan^(-1)(x))/(1-x)^2
8) (tan^(-1)(x) (d/dx(1)+d/dx(x)))/(1-x)+((x+1) (d/dx(tan^(-1)(x))))/(1-x)+((x+1) tan^(-1)(x))/(1-x)^2
9) (tan^(-1)(x) (d/dx(1)))/(1-x)+(tan^(-1)(x) (d/dx(x)))/(1-x)+(x+1)/((1-x) (x^2+1))+((x+1) tan^(-1)(x))/(1-x)^2
10) (tan^(-1)(x) (d/dx(x)))/(1-x)+(x+1)/((1-x) (x^2+1))+((x+1) tan^(-1)(x))/(1-x)^2
11) (x+1)/((1-x) (x^2+1))+((x+1) tan^(-1)(x))/(1-x)^2+(tan^(-1)(x))/(1-x)
Zadanie drugie a raczej b :)
Odpowiedź d/dx(x^2/(x^(3/3)+1)) = (2 x)/(x+1)-x^2/(x+1)^2
Rozwiązanie:
d/dx(x^2/(x+1))
1) (d/dx(x^2))/(x+1)-(x^2 (d/dx(x+1)))/(x+1)^2
2) (2 x)/(x+1)-(x^2 (d/dx(x+1)))/(x+1)^2
3) (2 x)/(x+1)-(x^2 (d/dx(1)+d/dx(x)))/(x+1)^2
4) (2 x)/(x+1)-(x^2 (d/dx(x)))/(x+1)^2
5) (2 x)/(x+1)-x^2/(x+1)^2
No i to tyle :)
Polecam Ci skrypty z zadaniami z pochodnymi z politechniki ;-)
Pozdro ;))