y=x3-4x2+5, find dydx,d2ydx2and d3ydx3

y=x3-4x2+5dydx=ddxx3-4x2+5=3x2-8xd2ydx2=ddx3x2-8x=6x-8d32ydx3=ddx6x-8=6

y=x3-4x2+5, find dydx,d2ydx2and d3ydx3

y=x3-4x2+5dydx=ddxx3-4x2+5=3x2-8xd2ydx2=ddx3x2-8x=6x-8d32ydx3=ddx6x-8=6

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$y = x^{3} - 4 x^{2} + 5, f i n d \frac{d y}{d x}, \frac{d^{2} y}{d x^{2}} a n d \frac{d^{3} y}{d x^{3}}$

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$(2 x^{2} - 8), (6 x - 4), 6$

$(3 x^{2} - 8 x), (6 x - 8), 6$

$(3 x^{2} - 8), (8 x - 6), 3$

$(3 x^{2} - 4 x), (4 x - 6), 4$

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Detailed Solution

$y = x^{3} - 4 x^{2} + 5$

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

$= 3 x^{2} - 8 x$

$\frac{d^{2} y}{d x^{2}} = \frac{d}{d x} (3 x^{2} - 8 x) = 6 x - 8$

$\frac{d^{32} y}{d x^{3}} = \frac{d}{d x} (6 x - 8) = 6$

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$y = x^{3} - 4 x^{2} + 5, f i n d \frac{d y}{d x}, \frac{d^{2} y}{d x^{2}} a n d \frac{d^{3} y}{d x^{3}}$