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211. Differentiate x² e^3x w.r.t. (log x)².

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212.

Differentiate space log space straight x space straight w. straight r. straight t space 1 over straight x

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213.

Differentiate space straight x squared space straight w. straight r. straight t space straight x cubed

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214. Differentiate log (x e^x) w.r.t. x log x.

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We space have space space space space space space space space space space space space space space space space space space straight x to the power of 6 plus straight y to the power of 6 plus 6 straight x squared straight y squared equals 16 Differentiating space both space sides space straight w. straight r. straight t space straight x comma space we space get comma space space space space space space space space space space space space space space space space space space space 6 straight x to the power of 5 plus 6 straight y to the power of 5 dy over dx plus 6 open parentheses straight x squared.2 straight y dy over dx plus straight y squared.2 straight x close parentheses equals 0 therefore space space space straight x to the power of 5 plus straight y to the power of 5 dy over dx plus 2 straight x squared straight y dy over dx plus 2 xy squared equals 0 therefore space space left parenthesis straight y to the power of 5 plus 2 straight x squared straight y right parenthesis dy over dx equals negative left parenthesis straight x to the power of 5 plus 2 xy squared right parenthesis therefore space space dy over dx equals negative fraction numerator straight x left parenthesis straight x to the power of 4 plus 2 straight y squared right parenthesis over denominator straight y left parenthesis straight y to the power of 4 plus 2 straight x squared right parenthesis end fraction

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216. Find

dy over dx

in the following :
x² + x y + y² = 100

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217. Find

dy over dx

in the following :
x³ + x² y + x y² + y³ = 81

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218.

Find space dy over dx space where space straight x squared over straight a squared plus straight y squared over straight b squared equals 2003

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219.

Find space dy over dx space where space 4 straight x squared plus 5 xy plus 7 straight y squared minus 8 straight x plus 9 straight y plus 3 equals 0.

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220.

Find space dy over straight d space where space straight x squared plus straight y squared equals 30 straight x space straight y

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