Derivatives Of Standard Functions
Gbogbo ọrọ náà
Differentiation measures how fast a quantity is changing at an instant, and almost all of it rests on a short list of standard derivatives. Once you know how to differentiate powers, the basic trigonometric functions, the exponential and the logarithm, the chain rule lets you handle the combinations that follow.
In this lesson you will learn the derivative notation, the rule \(\frac{d}{dx}x^n=nx^{n-1}\), the derivatives of \(\sin x\), \(\cos x\), \(e^x\) and \(\ln x\), and how the chain rule differentiates a composite. Angles for trigonometric derivatives are always measured in radians.
Ebumnobi
- Understand the idea of a derived function and use the notation f'(x), f''(x), dy/dx and the second derivative d2y/dx2.
- Know and use the derivatives of x to the power n (for any rational n), sin x, cos x, tan x, e to the power x and ln x, including the chain rule for composite functions.
Akọmọ Ojú-ẹkọ
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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.
- What is d/dx of x^5? A. 5x^4 B. x^4 C. 5x^6 D. 4x^5 Answer: A
- What is the derivative of cos x? A. sin x B. -sin x C. cos x D. -cos x Answer: B
- What is the derivative of e^x? A. x e^{x-1} B. e^x C. e^{x}/x D. 1 Answer: B
- Using the chain rule, d/dx of (2x + 1)^4 is: A. 4(2x + 1)^3 B. 8(2x + 1)^3 C. (2x + 1)^3 D. 8(2x + 1)^4 Answer: B
- With x in radians, d/dx of sin(3x) is: A. cos(3x) B. 3 cos(3x) C. -3 cos(3x) D. 3 sin(3x) Answer: B
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
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