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The quotient rule will need to be applied here.let u = sinx and let v = 2x+1du/dx = cosx and dv/dx =2thus using the quotient rule: (vdu/dx- udv/dx)/v^2(2xcosx +cosx - 2sinx)/ (2x+1)^2

There are two ways to solve this problem. The easiest way is graphically, but that requires little explanation and I am not sure how to show graphs on here so I will explain it algebraically.Because both ...

The first step is to differentiate the substitution.Because u=2+ln(t) we can differentiate to get du=(1/t) dt which can be rearranged to dt=t du.Once we have this we can start on the actual expression. We...

y=e^2x-9. When x=0 y=a.a=e²⁽⁰⁾-9a=1-9=-8.
When x=b y=0.0=e^2(b)-99=e^2bln(9)=ln(e^2b)ln(9)=2b(1/2)ln(9)=bln(9^(1/2))=bb=ln3

sec^2 x+ 2tan x = 0
use the fact that sec^2 x= tan^2 x +1
tan^2 x + 2tan x + 1 =0
(tan x +1)^2 = 0 tan x = - 1
x=3π/4, x= 7π/4