Please show all work so I can better understand! , Thank You 7.Consider the functions f, g: R → R² given by:f(t) = (t(2t – 3), te2t),g(t) = (-e2“, 1 – t²),for t E R.In(t)Also consider the function s: (0, 0) → R given by s(t)for t > 0.2(a)Find (f o s)'(t), for t > 0.(b)Find (f g)'(t), for t e R.

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7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te2t), g(t) = (-e2", 1– t²), for t e R. Also consider the function s: (0, 00) → R given by s(t) In(t) for t > 0. 2 (a) Find (f o s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.

7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te2t), g(t) = (-e2", 1– t²), for t e R. Also consider the function s: (0, 00) → R given by s(t) In(t) for t > 0. 2 (a) Find (f o s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)

Problem 29E

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Question

Please show all work so I can better understand!

, Thank You

7.
Consider the functions f, g: R → R² given by:
f(t) = (t(2t – 3), te2t),
g(t) = (-e2“, 1 – t²),
for t E R.
In(t)
Also consider the function s: (0, 0) → R given by s(t)
for t > 0.
2
(a)
Find (f o s)'(t), for t > 0.
(b)
Find (f g)'(t), for t e R.

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