Find differentiation of $(3 x^{4} + 2 x^{2} - 5 x) (4 x^{2} + 3 x)$ w.r.t $x$ .

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Solution

Consider the given polynomial.
$y = (3 x^{4} + 2 x^{2} - 5 x) (4 x^{2} + 3 x)$

On differentiating w.r.t $x$ , we get
$\frac{d y}{d x} = \frac{d}{d x} (3 x^{4} + 2 x^{2} - 5 x) (4 x^{2} + 3 x)$

$\frac{d y}{d x} = (4 x^{2} + 3 x) \frac{d}{d x} (3 x^{4} + 2 x^{2} - 5 x) + (3 x^{4} + 2 x^{2} - 5 x) \frac{d}{d x} (4 x^{2} + 3 x)$

$\frac{d y}{d x} = (4 x^{2} + 3 x) (12 x^{3} + 4 x - 5) + (3 x^{4} + 2 x^{2} - 5 x) (8 x + 3)$

Hence, this is the answer.

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