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Given, `y=(ax+b)^(2)` , evaluate ` (dy)/(dx)`. |
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Answer» Method I : Substituting (ax+b)=u Then `" "(du)/(dx)=(d(ax+b))/(dx)=a` and `" "(dy)/(du)=(d(ax+b)^(2))/(du)=(d(u)^(2))/(du)=2u` `:. " " (dy)/(dx)=(dy)/(du) xx (du)/(dx)=2u xx a =2 (ax+b)a` `" " =2a(ax+b)` Method II : `y=(ax+b)^(2)` `=a^(2)x^(2)+b^(2)+2abx` `"Then" " " (dy)/(dx)=(d)/(dx)[a^(2)x^(2)+b^(2) + 2abx]` `=(d)/(dx) (a^(2)x^(2))+(d)/(dx)(b^(2)) +(d)/(dx) (2abx)` `=a^(2)=(d(x)^(2))/(dx)+ 0+ 2ab(dx)/(dx)` `=a^(2)xx2x+2ab xx1` `=2a(ax+b)` |
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