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Continuity And Differentiability

Question

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Differentiate (3x² - 9 x + 5)⁹ w.r.t.x.

Solution

Let space space space space space space straight y equals left parenthesis 3 straight x squared minus space 9 space straight x space plus space 5 right parenthesis to the power of 9 therefore space dy over dx equals 9 left parenthesis 3 straight x squared space minus space 9 space straight x space plus space 5 right parenthesis to the power of 8. straight d over dx left parenthesis 3 straight x squared minus space 9 space straight x space plus space 5 right parenthesis space space space space space space space space space space space space space equals 9 left parenthesis 3 straight x squared minus space 9 space straight x space plus space 5 right parenthesis to the power of 8. left parenthesis 6 straight x minus 9 right parenthesis therefore space dy over dx equals 9 left parenthesis 6 straight x minus 9 right parenthesis left parenthesis 3 straight x squared space minus space 9 space straight x space plus space 5 right parenthesis to the power of 8

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