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Calculus/Trigonometric Differenciation
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Question
Hello, I was just wondering if you could help me answer these differentiation problems. I tried to complete them to the best of my ability but I am not sure if I completed them correctly. Thank You!
1. y=4sin3x^2
2. y=cos^3 4x
3. y=sin(x^2-x)
4. y=x^2cos3x
5. f(x)=sin(cosx)cos(sinx)
1. y=4[sin³(x²)] -> y'=4[sin³(x²)]'= 4*3[sin²(x²)]*cos(x²)*2x =
24x[cos(x²)]sin²(x²)].
I followed the rules :
a. f(g(x))'=f'(g(x))*g'(x)
b. f(g(h(x)))=f'(g(h(x)))*g'(h(x))*h'(x)
2. y=cos³(4x) -> y'=-3[cos²(x)]*[sin(x)]*4=-12[cos²(x)]*[sin(x)] .
3. y=sin(x²-x) -> y'=[cos(x²-x)][2x-1] .
4. y=x²[cos3x] -> y'=2x[cos3x]+x²[-sin3x]*3=6x[cos3x]-x²[sin3x] .
I followed the rule : [fg]'=f'g+fg'
5. f(x) = sin(cosx) * cos(sinx)
1st : sin(cosx)'=cos(cosx)*[-sinx]=-[sinx][cos(cosx)] .
2nd : cos(sinx)'=-sin(sinx)*[cosx]=-[cosx][sin(sinx)] .
So,
f'(x)=sin(cosx)' * cos(sinx) + sin(cosx) * cos(sinx)'
f'(x)=-[sinx][cos(cosx)]*cos(sinx)-sin(cosx)*[cosx][sin(sinx)] .
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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