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Calculus/Trignomentric derivative

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Expert: Alon Mandes - 3/2/2011


Question
QUESTION: differentiate cos(sinx)((cosx))

ANSWER: { [cos(sin(x))]*[cos(x)] }' = [cos(sin(x))]'*[cos(x)]+[cos(sin(x))]*[cos(x)]' =
cos(sin(x))*[-sin(x)]*[cos(x)]+[cos(sin(x))]*[-sin(x)]=
[-sin(x)] * { cos(sin(x)) + cos(x) } .

Alon.

---------- FOLLOW-UP ----------

QUESTION: Hi Alon

If y = sin (sinx) show that y" + y'tanx + y cos(square)x = 0

Answer
sorry , correction :
{ [cos(sin(x))]*[cos(x)] }' = -[sin(x)]*[cos(sin(x))] - [cosē(x)][sin(sin(x))] .
Thus,

y = sin((sin(x))

Let's derive 1st time : y'=[cos(sin(x))]*[cos(x)] .

Now, let's derive 2nd time :
y''={ cos(sin(x))*[cos(x)] }' = -[sin(x)]*[cos(sin(x))] - [cosē(x)][sin(sin(x))] .

Thus,

y'*tan(x) = [cos(sin(x))]*[cos(x)]*[sin(x)/cos(x)] = [sin(x)][cos(sin(x))] .

y*cosē(x) = [cosē(x)]*[sin(sin(x))]

Therefore :
y''+y'*tan(x)+y*cosē(x)=
-[sin(x)]*[cos(sin(x))]-[cosē(x)][sin(sin(x))]+[sin(x)][cos(sin(x))]+[cosē(x)]*[sin(sin(x))] .

= -[cosē(x)][sin(sin(x))]+[cosē(x)]*[sin(sin(x))] = 0

Alon.  

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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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