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Understanding Differentiation In Mathematics

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PDF 436.79 KB 15 pages Jul 23, 2026
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TOPIC 3: DIFFERENTIATION Tangents and Normal A gradient of a curve at a point Defined as the gradient of the ta ngent to the curve at the point To find a gradient at a point you need to get a point next to the given point and use y - increase over x -increase If A is the required point then B in the point next to A. The closer B is to A the better the approximation Gradient chord of AB is approximately equal to gradient at A. Tha t is to say the gradient of AB as B tends to A will equal to the gradient at A Note the Delta prefix yin increase Smallyxin increase smallax  Consider the curve y=x2 y=x2 B( ) , y yx x A(x,y) As y tends to zero  xy grad which dxdy 2) ( x x y y  2 2)( 2 x xx xy y  y x xx xy 2 2)( 2 2 2 2)( 2 x x xx xy  2)( 2 x xx y  xy xx xyy yGrad )( 2 x xxy 0y As x gradx x x andgradxy 22 2  3xy For 3) ( x x y y  3 2 2 3)()(3 3 x xx xx xy y  3 3 2 2 3)()(3 3 x x xx xx xy  2 2)( 3 3 x xx xxxy As 0), 3,02 xxx x 23x grad This implies that for the curve y= xn Its grad = nxn-1 EXAMPLE 1 Finding the grad function of the curve y = 2x(x- 4) = 2x2-8x ) (8- ) (2x x x xy y   x x x xx x y y  8 8- )( 2 (22 2 x x x x x xx …
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Understanding Differentiation In Mathematics , is an educational document on StudyUganda.com. This resource includes: "TOPIC 3: DIFFERENTIATION Tangents and Normal A gradient of a curve at a point Defined as the gradient of the ta ngent to the curve ……" (Format: PDF) — 436.79 KB, 15 pages. Added July 23, 2026.

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