Differentiation
Gbogbo ọrọ náà
Differentiation is the mathematics of slopes and change. It gives you the gradient of a curve at any point, not just a straight line, and that single idea lets you find where a curve is steepest, where it turns, and where a quantity is at its maximum or minimum.
In this lesson (Extended tier) you will estimate gradients by drawing tangents, differentiate functions of the form a x to the power n, and use the derivative to find gradients and stationary (turning) points, telling maxima from minima.
Ebumnobi
- Estimate gradients of curves by drawing tangents.
- Use the derivatives of functions of the form axn, where a is a rational constant and n is a positive integer or zero, and simple sums of not more than three of these.
- Apply differentiation to gradients and stationary points (turning points).
- Discriminate between maxima and minima by any method.
Nkuzi Olu
Gee ntị na nkuzi a na ngwa
Maapụ uche
E seela isiokwu a ka ị hụ otu echiche si ejikọta.
Mepee maapụ uche na ngwa
Kaadị ncheta
Omume ncheta ngwa ngwa n'ihe a na-anwale n'isiokwu a.
Mee omume kaadị ndị a na ngwa
Akwụkwọ Ọmụmụ
Ndetu Nkuzi Zuru Ezu di na Ngwa Green Bridge
Nweta ngwa Green Bridge CBT na ekwenti gi ma o bu kompiuta maka ulo akwukwo IGCSE zuru oke: akwukwo ule ndi gara aga, usoro nyocha, eserese uche, kaadi omumu na nkuzi olu.
Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Differentiation. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- Differentiate y = x^2. A. 2x B. x C. 2x^2 D. 2 Answer: A
- For y = x^2, what is the gradient at x = 2? A. 2 B. 4 C. 8 D. 1 Answer: B
- Differentiate y = 3x^2. A. 3x B. 6x C. 6x^2 D. 9x Answer: B
- At a turning point, the gradient dy/dx is: A. 1 B. negative C. zero D. undefined Answer: C
- For y = x^2 - 4x + 1, at what value of x is the turning point? A. x = 1 B. x = 2 C. x = 4 D. x = -2 Answer: B
Rue ajuju ndi a n'ime ngwa ahu
Rue ajuju ndi a n'ime ngwa ahu
Akwụkwọ A Na-atụ Aro
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Differentiation? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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