trigonometric problems....plzzzzz solve...?

Question

1. tan^-1 {(1+x^2)^1/2 -1 / x} w.r.t. sin^-1 (2x / 1+x^2)
2.cos^-1 (1-x^2 / 1+x^2) w.r.t. tan^-1 x

Answer 1

well thats simple....use parametric differentiation,i.e, in d first question let the tan inverse term be y and the sin inverse term be z. You need to find dy/dz which is also equal to (dy/dz)(dx/dx) = (dy/dx)/(dz/dx)

So differentiate y and z wrt x (the common variable) and divide the derivative of y with the derivative of z...the 2nd part can be attempted similarly. Hope it helps!!

Answer 2

just do the chain rule: Vdu + udv

or quotient (vdu-udv)/v^2



should be easyy

and if there's no need to simplyfy it'll be easy just times out the brack then difereniate them then times it with the tan -1 then plus the other way etc





ooh seen i thought it was tan to the power of minus one instead of inverse, mate if you can't do it check your books why should i just tell you the answer?

Answer 3

if the functions are u and v

find du/dx , dv/dx, then take their ratio

you could use trigonometric substitution to simplify and then differentiate

use the following link for explanation of the second problem

http://rbmix.com/problem/math/fc/fc.html

Answer 4

plz apply chain rule.

Answer 5

get a tutor