Real number units = 1
Imaginary number units = i = √−1
−2+−544343=−2−544343=−544345
Hope that helps.
(−13)(21)=−213=−7
5^1 mod 8 = 5
5^2 mod 8 = 1
5^3 mod 8 = 5
therefore 5^(2n+1) mod 8 = 5
therefore 5^137 mod 8 = 5.
h′(1)=1√1+12=√22
g′(1)=(e1)((1+12)(1+1)+2(1)2)=6e
f′(1)=12−15(1)2(ln1)=1
ddx√1+x2h=√uu=1+x2dhdx=dhdu×dudx=12√1+x2×2x=x√1+x2
ddx(1+xex(1+x2))
=ddx1+(1+x2)ddxxex+(xex)ddx(1+x2)
=(1+x2)(ex)(1+x)+(x)(ex)(2x)
=(ex)((1+x2)(1+x)+2x2)
ddx(1−x3(5lnx+2))
=ddx1−ddx5x3lnx+ddx2x3
=ddx2x3−(5x3)ddxlnx−(lnx)ddx5x3
=6x2−(5x3)(1x)−(lnx)(15x2)
=6x2−5x2−15x2lnx
=x2−15x2lnx