4ORCE Posted February 23, 2007 Share Posted February 23, 2007 If y=x + sin(xy) then dy/dx equals.... I don't understand how you take the derivative of sin(xy). I think you have to use the multiplication rule and get x dy/dx + y But what do you do from there? Link to comment Share on other sites More sharing options...

ydoaPs Posted February 23, 2007 Share Posted February 23, 2007 Use the chain rule. Link to comment Share on other sites More sharing options...

frostbite Posted February 27, 2007 Share Posted February 27, 2007 If y=x + sin(xy) then dy/dx equals.... I don't understand how you take the derivative of sin(xy). I think you have to use the multiplication rule and get x dy/dx + y But what do you do from there? your function is quite hard to answer since it will go on a circle. if we try to substitute y in x + sin(xy) we still have y. it is also quite hard since we have two variables. though i haven't answered it yet, these are some of my points regarding your question. i'll try to solve this later. hope i can answer it. till next time! Link to comment Share on other sites More sharing options...

D H Posted February 27, 2007 Share Posted February 27, 2007 if we try to substitute y in x + sin(xy) we still have y. Don't do that then. Use implicit differentiation, as the title of the thread suggests. The derivative of the left-hand side is simply dy/dx. Use the chain rule to get an expression involving dy/dx on the right-hand side. Collect terms and solve for dy/dx. Link to comment Share on other sites More sharing options...

frostbite Posted March 2, 2007 Share Posted March 2, 2007 Don't do that then. Use implicit differentiation, as the title of the thread suggests. The derivative of the left-hand side is simply dy/dx. Use the chain rule to get an expression involving dy/dx on the right-hand side. Collect terms and solve for dy/dx. yeah.. that's how to get the answer.. I guess.. y = x + sin(xy) dy/dy = 1 + cos(xy) * (y + x dy/dx) (Use of Chain Rule) dy/dx = 1 + y cos(xy) + x dy/dx cos(xy) [dy/dx-(x dy/dx cos(xy))] = 1 + y cos(xy) dy/dx [1 - x cos(xy)] = 1 + y cos(xy) (simplifying the equation we arrive to..) dy/dx = [1 + y cos(xy)]/[1 - x cos(xy)] ---> my answer... hope its correct.. hek hek hek!! xiao! Link to comment Share on other sites More sharing options...

A Fool Posted June 10, 2007 Share Posted June 10, 2007 I Derived the same answer...... Link to comment Share on other sites More sharing options...

cosine Posted June 11, 2007 Share Posted June 11, 2007 If y=x + sin(xy) dy = dx + cos(xy)*(ydx + xdy) dy(1 - x*cos(xy)) = dx(1 + y*cos(xy)) so y'= (1 + y*cos(xy))/(1 - x*cos(xy)) yep Link to comment Share on other sites More sharing options...

frostbite Posted June 11, 2007 Share Posted June 11, 2007 If y=x + sin(xy) dy = dx + cos(xy)*(ydx + xdy) dy(1 - x*cos(xy)) = dx(1 + y*cos(xy)) so y'= (1 + y*cos(xy))/(1 - x*cos(xy)) yep wahehe!! i like your signature. hehe!! so who's lying among the three (A, B, C)? hehe!! i bet its D! Link to comment Share on other sites More sharing options...

cosine Posted June 11, 2007 Share Posted June 11, 2007 wahehe!! i like your signature. hehe!! so who's lying among the three (A, B, C)? hehe!! i bet its D! Depending on how you interpret the question, its B, if they happen to all know the answer, or there is no answer if they don't know the answer. Link to comment Share on other sites More sharing options...

frostbite Posted June 12, 2007 Share Posted June 12, 2007 Depending on how you interpret the question, its B, if they happen to all know the answer, or there is no answer if they don't know the answer. indeed, it is B. hehe! awww... how come no one laughed at my joke... nah! it was not even a joke. 'twas just a stupid post.. Link to comment Share on other sites More sharing options...

cosine Posted June 16, 2007 Share Posted June 16, 2007 indeed, it is B. hehe! awww... how come no one laughed at my joke... nah! it was not even a joke. 'twas just a stupid post.. Oh I see the joke now... lolz Link to comment Share on other sites More sharing options...

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