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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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Let space straight y equals straight x cubed comma space straight u equals straight x cubed therefore space space space space space dy over dx equals 2 straight x comma space du over dx equals 3 straight x squared Now space dy over dx equals fraction numerator begin display style dy over dx end style over denominator begin display style du over dx end style end fraction equals fraction numerator 2 straight x over denominator 3 straight x squared end fraction equals fraction numerator 2 over denominator 3 straight x end fraction

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

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215.

Find space dy over dx space if 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.

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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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