Q. 174.1( 38 Votes )

# Differentiate (x<

Answer :

Given: (x^{2} – 5x + 8) (x^{3} + 7x + 9)

Let y=(x^{2} – 5x + 8) (x^{3} + 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 = (x^{2} – 5x + 8) (x^{3} + 7x + 9)

y = x^{5} + 7x^{3} + 9x^{2} - 5x^{4} – 35x^{2} - 45x + 8x^{3} + 56x + 72

y = x^{5} - 5x^{4} + 15x^{3} - 26x^{2} + 11x + 72

Now, differentiate both sides with respect to x

(iii) by logarithmic differentiation

y = (x^{2} – 5x + 8) (x^{3} + 7x + 9)

Taking log on both sides, we get

log y = log ((x^{2} – 5x + 8) (x^{3} + 7x + 9))

log y = log (x^{2} – 5x + 8) + log (x^{3} + 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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