Answer :

Given: (x2 – 5x + 8) (x3 + 7x + 9)

Let y=(x2 – 5x + 8) (x3 + 7x + 9)


(i) By applying product rule differentiate both sides with respect to x







(ii) by expanding the product to obtain a single polynomial


y = (x2 – 5x + 8) (x3 + 7x + 9)


y = x5 + 7x3 + 9x2 - 5x4 – 35x2 - 45x + 8x3 + 56x + 72


y = x5 - 5x4 + 15x3 - 26x2 + 11x + 72


Now, differentiate both sides with respect to x




(iii) by logarithmic differentiation


y = (x2 – 5x + 8) (x3 + 7x + 9)


Taking log on both sides, we get


log y = log ((x2 – 5x + 8) (x3 + 7x + 9))


log y = log (x2 – 5x + 8) + log (x3 + 7x + 9)


Now, differentiate both sides with respect to x










From equation (i),(ii)and(iii), we can say that value of given function after differentiating by all the three methods is same.


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