Question

$x ^{2} \sin(2x)$

Answer 1

$\underline{ \large{ \text{Answer}}} : \\ \\ \text{Let, y = } { \text{x}}^{2} \text{sin2x} \\ \\ \text{Now, differentiating both sides w. r. to x, we get} \\ \\ \frac{ \text{dy}}{ \text{dx}} = \frac{ \text{d}}{ \text{dx}} ( { \text{x}}^{2} \text{sin2x}) \\ \\ = { \text{x}}^{2} \: \frac{ \text{d}}{ \text{dx}} \text{(sin2x)} + \text{sin2x} \: \frac{ \text{d}}{ \text{dx}} \: ( {{ \text{x}}^{2}} ) \\ \\ = { \text{x}}^{2} \text{cos2x} + \text{2x sin2x} \\ \\ \implies \boxed{ \frac{ \text{dy}}{ \text{dx}} = { \text{x}}^{2} \text{cos2x} + \text{2x sin2x}}$

$\underline{ \large{ \text{Rule}} }: \\ \\ \text{1.} \: \: \: \frac{ \text{d}}{ \text{dx}} \text{(sin mx)} = \text{m cos mx} \\ \\ \text{2.} \: \: \frac{ \text{d}}{ \text{dx}} \: \: ( { \text{x}}^{\text{n}} ) = \text{n} \: { {\text{x}}^{\text{n - 1}} } \\ \\ \bigstar \: \underline{ \text{MarkAsBrainliest}} \: \bigstar$