If y-3x2-2x then dy dx-

Dy dx=d dx[3x^2]+d dx[2x] (Using the linearity property of differentiation) dy dx=3d[x^2] dx+2d[x] dx (Separating the constant coefficients) =3 × 2 x^2 1+2×1x^ ...

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Standard XII

Physics

Basic Differentiation Rule

If y=3x2+2x t...

Question

If $y = 3 x^{2} + 2 x t h e n \frac{d y}{d x}$ =?

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$3 x^{2} + 2 x$

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6x + 2

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none of these

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Solution

The correct option is C
6x + 2

$\frac{d y}{d x} = \frac{d}{d x} [3 x^{2}] + \frac{d}{d x} [2 x]$ (Using the linearity property of differentiation)

$\frac{d y}{d x} = 3 \frac{d [x^{2}]}{d x} + 2 \frac{d [x]}{d x}$ (Separating the constant coefficients)
= $3 \times 2 x^{2 - 1} + 2 \times 1 x^{1 - 1}$ =6x+2(using $\frac{d [x^{n}]}{d x} = n . x^{n - 1}$ )

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If y=3x2+2x then dydx=?

The correct option is C 6x + 2 dydx=ddx[3x2]+ddx[2x] (Using the linearity property of differentiation) dydx=3d[x2]dx+2d[x]dx (Separating the constant coefficients) =3×2 x2−1+2×1x1−1 =6x+2(using d[xn]dx=n.xn−1)

If $y = 3 x^{2} + 2 x t h e n \frac{d y}{d x}$ =?