Question

use the following to complete the problems
d/dx(sin^(-1)u=(1-u^2)^-1/2(du/dx)
d/dx(tan^(-1)u=(1+u)^-1(du/dx)

A)y=sin^-1(e^x)
B)y=sin^-1[e^(sin^(-1)x]
c) y=[tan^-1(x)](1+x^2)

I'm not sure what to do at all

Answer 1

chain rule for each

Answer 2

so for example, the first one write down the derivative of arcsine, only replace \(x\) by \(e^x\)
then multiply your answer by the derivative of \(e^x\) which is \(e^x\)

Answer 3

first one you get
\[\frac{1}{\sqrt{1-(e^x)^2}}\times e^x=\frac{e^x}{\sqrt{1-e^{2x}}}\]

Answer 4

thank you for your help