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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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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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Here space straight x squared plus straight y squared equals 30 straight x space straight y Differentiating space both space sides space straight w. straight r. straight t space space straight x comma space we space get comma space space space space space space space space 3 straight x squared plus 2 straight y dy over dx equals 30 straight x dy over dx plus 30 straight y.1 therefore left parenthesis 2 straight y minus 30 straight x right parenthesis dy over dx equals 30 straight y minus 3 straight x squared therefore space space space space space space space space space space space space space dy over dx equals fraction numerator 3 left parenthesis 10 straight y minus straight x squared right parenthesis over denominator 2 left parenthesis straight y minus 15 straight x right parenthesis end fraction

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