Q17 (2)   Differentiate (x^2 - 5x + 8) (x^3 + 7x + 9) in three ways mentioned below:
                (ii) by expanding the product to obtain a single polynomial.

Answers (1)

Given function is
f(x)=(x^2 - 5x + 8) (x^3 + 7x + 9)
Multiply both to  obtain a single higher degree polynomial
f(x) = x^2(x^3+7x+9)-5x(x^3+7x+9)+8(x^3+7x+9)
            = x^5+7x^3+9x^2-5x^4-35x^2-45x+8x^3+56x+72
            = x^5-5x^4+15x^3-26x^2+11x+72
Now, differentiate w.r.t. x
we get,
f^{'}(x)=5x^4-20x^3+45x^2-52x+11
Therefore, the answer is 5x^4-20x^3+45x^2-52x+11
 

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