If y - 3x2 - 2x- then find dydx-

dydx = ddx [3x^2] + ddx [2x] (Using the linearity property of differentiation) dydx = 3d[x^2]dx + d[x]dx (Separating the constant coefficients) =3 ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Derivatives

If y = 3x2 ...

Question

If $y = 3 x^{2} + 2 x$ , then find $\frac{d y}{d x}$ .

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Solution

$\frac{d y}{d x} = \frac{d}{d x} [3 x^{2}] + \frac{d}{d x} [2 x]$
(Using the linearity property of differentiation)
$\frac{d y}{d x} = 3 \frac{d [x^{2}]}{d x} + \frac{d [x]}{d x}$ (Separating the constant coefficients)
$= 3 \times 2 x^{2 - 1} + 2 \times 1 x^{1 - 1} = 6 x + 2$
$(U s i n g \frac{d [x^{n}]}{d x} = n x^{n - 1})$ .

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If y=3x2+2x, then find dydx.

dydx=ddx[3x2]+ddx[2x](Using the linearity property of differentiation)dydx=3d[x2]dx+d[x]dx (Separating the constant coefficients)=3×2x2−1+2×1x1−1=6x+2(Usingd[xn]dx=nxn−1).

If $y = 3 x^{2} + 2 x$ , then find $\frac{d y}{d x}$ .