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straight x equals 2 at squared comma space straight y equals at to the power of 4 therefore space dx over dt equals 4 at comma space dy over dt equals 4 at cubed Now space dy over dx equals fraction numerator dx over dt over denominator dy over dt end fraction equals fraction numerator 4 at over denominator 4 at cubed end fraction equals straight t squared

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202.

If space straight x equals straight a open parentheses fraction numerator 1 plus straight t squared over denominator 1 minus straight t squared end fraction close parentheses space and space straight y equals fraction numerator 2 straight t over denominator 1 minus straight t squared end fraction comma space find space dy over dx.

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203.

If space straight x equals fraction numerator 1 minus straight t squared over denominator 1 plus straight t squared end fraction comma space straight y equals fraction numerator 2 straight t over denominator 1 plus straight t squared end fraction comma space prove space that space dy over dx plus straight x over straight y equals 0.

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204.

Find space dy over dx space where space straight x equals fraction numerator straight a left parenthesis 1 minus straight t squared right parenthesis over denominator 1 minus straight t squared end fraction comma space straight y space equals fraction numerator 2 bt over denominator 1 minus straight t squared end fraction

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205.

Find space dy over dx space when space straight x equals straight e to the power of straight t. space log space straight t comma space straight y equals straight t. log space straight t.

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206.

Find space dy over dx when space straight x equals fraction numerator 3 at over denominator 1 plus straight t cubed end fraction comma space straight y equals fraction numerator 3 at squared over denominator 1 plus straight t cubed end fraction

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207.

If space space straight x equals fraction numerator 3 at over denominator 1 plus straight t squared end fraction comma space straight y equals fraction numerator 3 at squared over denominator 1 plus straight t squared end fraction comma space then space find space dy over dt space at space straight t equals 2

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208.

If space straight x equals fraction numerator 1 plus log space straight t over denominator straight t squared end fraction comma space straight y equals fraction numerator 3 plus 2 space log space straight t over denominator straight t end fraction comma space straight t greater than 0 comma space prove space that space straight y dy over dx minus 2 straight x open parentheses dy over dx close parentheses squared equals 1

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209.

For space straight a space positive space constant space straight a space find space dy over dx comma space where space straight y equals straight a to the power of straight t plus 1 over straight t end exponent comma space and space straight x equals open parentheses straight t plus 1 over straight t close parentheses to the power of straight a.

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210. Differentiate 7x⁵ - 11 x² w.r.t. 7x² - 15 x

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