Differentiate (x^2– 5x + 8) (x^3 + 7x + 9) in three ways mentione… - Vidyadip

Question

Differentiate $(x^2– 5x + 8) (x^3 + 7x + 9)$ in three ways mentioned below:
by using product rule

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Answer

Let $y = (x^2- 5x + 8)(x^3 + 7x + 9) ....(i)$
$\frac{\text{dy}}{\text{dx}}=(\text{x}^2-5\text{x}+8)\frac{\text{d}}{\text{dx}}(\text{x}^3+7\text{x}+9)+(\text{x}^3+7\text{x}+9)\frac{\text{d}}{\text{dx}}(\text{x}^2-5\text{x}+8)$
$\Rightarrow\ \frac{\text{dy}}{\text{dx}}=(\text{x}^2-5\text{x}+8)(3\text{x}^2+7)+(\text{x}^3+7\text{x}+9)(2\text{x}-5)$
$\Rightarrow\ \frac{\text{dy}}{\text{dx}}=3\text{x}^4+7\text{x}^2-15\text{x}^3-35\text{x}+24\text{x}^2+56+2\text{x}^4-5\text{x}^3+14\text{x}^2-35\text{x}+18\text{x}-45$
$\Rightarrow\ \frac{\text{dy}}{\text{dx}}=5\text{x}^4-20\text{x}^3+45\text{x}^2+11\ \dots\text{(ii)}$

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