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Continuity and Differentiability

Short Answer Type

221.

Find space dy over dx space where space xy equals 100 left parenthesis straight x plus straight y right parenthesis

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222.

Find space dy over dx comma space where space straight y left parenthesis straight y plus 1 right parenthesis equals straight x left parenthesis straight x plus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis

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223.

Find space dy over dx space where space left parenthesis straight x squared minus straight y squared right parenthesis squared equals 4 xy

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224.

Find space dy over dx where space square root of straight x plus square root of straight y equals 20

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225.

Find space dy over dx where space space space ax squared plus 2 hxy plus by squared plus 2 gx plus 2 fy plus straight c equals 0

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226.

Find space dy over dx space where space xy squared minus straight x squared straight y equals 4

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227. $Find space dy over dx space where space xy space log space left parenthesis straight x plus straight y right parenthesis equals 1$

Here space space xy space log space left parenthesis straight x plus straight y right parenthesis equals 1 Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma xy dy over dx left square bracket log left parenthesis straight x plus straight y right parenthesis right square bracket plus straight x space log space left parenthesis straight x plus straight y right parenthesis. straight d over dx left parenthesis straight y right parenthesis plus straight y space log space left parenthesis straight x plus straight y right parenthesis straight d over dx left parenthesis straight x right parenthesis equals 0 therefore xy fraction numerator 1 plus begin display style dy over dx end style over denominator straight x plus straight y end fraction plus straight x space log space left parenthesis straight x plus straight y right parenthesis. dy over dx plus straight y space log space left parenthesis straight x plus straight y right parenthesis.1 equals 0 therefore xy plus xy dy over dx plus straight x left parenthesis straight x plus straight y right parenthesis space log left parenthesis straight x plus straight y right parenthesis dy over dx plus straight y left parenthesis straight x plus straight y right parenthesis log left parenthesis straight x plus straight y right parenthesis equals 0 therefore left square bracket xy plus straight x left parenthesis straight x plus straight y right parenthesis log left parenthesis straight x plus straight y right parenthesis right square bracket dy over dx equals negative left square bracket xy plus straight y left parenthesis straight x plus straight y right parenthesis log left parenthesis straight x plus straight y right parenthesis right square bracket therefore dy over dx equals negative fraction numerator xy plus straight y left parenthesis straight x plus straight y right parenthesis log left parenthesis straight x plus straight y right parenthesis over denominator xy plus straight x left parenthesis straight x plus straight y right parenthesis log left parenthesis straight x plus straight y right parenthesis end fraction

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228.

Find space dy over dx where space space xy plus xe to the power of negative straight y end exponent plus ye to the power of straight x equals straight x squared

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229.

Find space dy over dx when space xy plus xe to the power of negative straight y end exponent plus ye to the power of straight x equals straight x squared

81 Views

230.

Find space dy over dx space when space ax squared plus 2 hx space plus by squared plus 2 gx plus 2 fy plus straight c equals 0

81 Views