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Sponsor Area

Continuity And Differentiability

Question

$If space straight y equals straight t squared plus straight t cubed space and space straight x equals straight t minus straight t to the power of 4 comma space find space dy over dx$

Solution

Here space straight y equals straight t squared plus straight t cubed comma space straight x equals straight t minus straight t to the power of 4 therefore space dy over dt equals 2 straight t plus 3 straight t squared comma space dx over dt equals 1 minus 4 straight t cubed space space space space space space dy over dx equals fraction numerator dy over dt over denominator dx over dt end fraction equals fraction numerator 2 straight t plus 3 straight t squared over denominator 1 minus 4 straight t cubed end fraction