# Implicit Diff.

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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?

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Use the chain rule.

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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!

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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.

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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!

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• 3 months later...

I Derived the same answer...... ##### Share on other sites

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

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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! ##### Share on other sites

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.

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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.. ##### Share on other sites

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

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