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Can someone help me with these questions?

1) find dy/dx of the following equations:

A) xy = sin^2 (y)
B) tan(2x+y) = x
C) e^(xy) = 4
Reply 1
Original post by Improvement
Can someone help me with these questions?

1) find dy/dx of the following equations:

A) xy = sin^2 (y)
B) tan(2x+y) = x
C) e^(xy) = 4

Have you studied implicit differentiation? What have you tried so far?
I would suggest over viewing implicit differentiation where you differentiate y within the equation, as in not separated on one side. Then apply the respective rules for differentiating.

Alternatively you could try and differentiate with respect to y and see where that takes you.
Reply 3
Yeah I completely forgot about that, I have the answer to the first and second one but for the middle one i get sec^2 instead of cos^2?
Reply 4
Original post by Improvement
Yeah I completely forgot about that, I have the answer to the first and second one but for the middle one i get sec^2 instead of cos^2?

Can you post your working and answer?
Original post by Improvement
Can someone help me with these questions?

1) find dy/dx of the following equations:

A) xy = sin^2 (y)
B) tan(2x+y) = x
C) e^(xy) = 4


Look up implicit differnetation and then post your workings with answers :smile:
B) gives sec^2(2x+y)*(2+dy/dx)=1 -> 2+dy/dx=1/sec^2(2x+y)=cos^2(2x+y) -> dy/dx = cos^2(2x+y)-2.

Original post by Improvement
Yeah I completely forgot about that, I have the answer to the first and second one but for the middle one i get sec^2 instead of cos^2?
Reply 7
Original post by constellarknight
B) gives sec^2(2x+y)*(2+dy/dx)=1 -> 2+dy/dx=1/sec^2(2x+y)=cos^2(2x+y) -> dy/dx = cos^2(2x+y)-2.

Please don't post full solutions. It's against the rules of the forum and far more beneficial to guide to a solution.

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