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Calculus/implicit differentiation

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Expert: Alon Mandes - 3/18/2010


Question
If, sin(xy)=x, then dy/dx=

Answer
1st of let's review some facts regarding implicit derivation :
1. If y=f(x) then d/dx { f(x) } = f'(x) . This can be also presented as :
   d/dx { y=f(x) } --> d/dx {y} = d/dx {f(x)} --> y'=f'(x) .
2. If y²=f(x) then : d/dx { y²=f(x) } --> d/dx {y²} = d/dx {f(x)} --> 2yy'=f'(x)
  --> y'=f'(x)/2y .
Thus,
sin(xy)=x
d/dx { Sin(xy)=x } --> d/dx {Sin(xy)} = d/dx {x} --> yCos(xy)+xy'Cos(xy)=1 -->
y'=[1-yCos(xy)]/[xCos(xy)] .

We used the rule : Sin[fg]'=f'Sin[fg]+g'Sin[fg]

Alon.

Calculus

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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".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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