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Calculus/limits and derivates
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Question
part(a):
given that:
f(x)= h(x)x^5
h(-1)= 4
h'(-1)= 7
find f'(-1)
part(b):
differentiate the following function:
f(t)=tsec(t)/1+ t^2
part(a):
We use the rule : [fg]'=f'g+fg' . Therefore,
f(x)= h(x)*x^5
f'(x)=h'(x)*x^5+h(x)*5x^4
f'(-1)=h'(-1)*(-1)^5+h(-1)*5*(-1)^4
=7 *(-1) +4*5*1
=-7+20=13
part(b):
f(t)=[t*sec(t)]/[1+ t^2]
We use the rule : [f/g]'=[f'g-fg']/g^2 .
We also know that the derivative of sec(t) is sec(t)tan(t) .
Therefore,
f'(t)=
[t*sec(t)]'*[1+t^2] - [t*sec(t)]*[1+t^2]'
------------------------------------------- =
[1+t^2]^2
[sec(t)+t*sec(t)*tan(t)]*[1+t^2] - [t*sec(t)]*[2t]
------------------------------------------------------ =
[1+t^2]^2
sec(t)+t*sec(t)*tan(t)+(t^2)*sec(t)+(t^3)*sec(t)*tan(t)] - (2t^2)*sec(t)
-------------------------------------------------------------------------- =
[1+t^2]^2
Alon.
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Answers by Expert:
Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience
1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
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