Question

evaluate dy/dx if y=3x^2+2x(x+9)​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ derivative \: of \: \: y \: \: w.r.t \: \: x \: \: of \\ y = 3x {}^{2} + 2x(x + 9) \\ \\ we \: know \: that \\ derivative \: of \: any \: polynomial \\ expression \: \: is \: given \: by \\ \\ \frac{dy}{dx} = n.x {}^{n - 1} \\ \\ \frac{dy}{dx} \: [ \: 3x {}^{2} + 2x(x + 9) \: ] \\ \\ = \frac{dy}{dx} (3x {}^{2} ) + \frac{dy}{dx} (2x(x + 9) \\ \\ = [ \: 3. \times 2x {}^{2 - 1} \: ] + \frac{dy}{dx} \: (2x {}^{2} + 18x) \\ \\ = 6x {}^{1} +( \: 2.2x {}^{2 - 1} + 18.1x {}^{1 - 1} \: ) \\ \\ = 6x + 4x + 18x {}^{0} \\ \\ = 10x + 18(1) \\ \\ = 10x + 18$