Differentiate the following function with respect to (x):(2x^2+1)… - Vidyadip

Question

Differentiate the following function with respect to $(\text{x})$:$(2\text{x}^2+1)(3\text{x}+2)$

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Answer

We have,$\frac{\text{d}}{\text{dx}}(2\text{x}^2+1)(3\text{x}+2)$
$=(3\text{x}+2)\frac{\text{d}}{\text{dx}}(2\text{x}^2+1)+(\text{2x}^2+1)\frac{\text{d}}{\text{dx}}(3\text{x}+2)$ [Using product rule]
$=(3\text{x}+2)(4\text{x}+0)+(\text{2x}^2+1)(3+0)$
$=(12\text{x}^2+\text{8x}+\text{6x}^2+3)$
$=18\text{x}^2+\text{8x}+3$

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