Differentiation
Akopọ
Differentiation is the mathematical tool that captures how a quantity changes at every instant. Whether you need the slope of a curve, the velocity of a moving object, or the rate at which a chemical reacts, the derivative is the single idea that answers all of these questions in one framework.
In this topic you will master the power rule, learn to differentiate trigonometric, exponential and composite functions, and apply the product, quotient and chain rules to handle combinations of functions that arise throughout the 4PM1 specification and beyond.
Awọn Afojusun
- Differentiate sums of multiples of powers of x, sin ax, cos ax and e^(ax)
- Differentiate a product of two functions
- Differentiate a quotient of two functions
- Differentiate simple cases of a function of a function (chain rule)
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Oriire fun ipari ẹkọ lori Differentiation. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- What is the derivative of y = 5x^3? A) 5x^2 B) 15x^2 C) 3x^2 D) 15x^3 Answer: B
- What is the derivative of y = sin 4x? A) cos 4x B) 4cos 4x C) -4cos 4x D) 4sin 4x Answer: B
- The product rule states that d/dx[uv] equals: A) u(dv/dx) - v(du/dx) B) u(dv/dx) + v(du/dx) C) (du/dx)(dv/dx) D) uv(du/dx + dv/dx) Answer: B
- What is the derivative of y = e^(3x)? A) e^(3x) B) 3xe^(3x) C) 3e^(3x) D) e^(3x)/3 Answer: C
- Using the chain rule, the derivative of y = (2x + 1)^5 is: A) 5(2x + 1)^4 B) 10(2x + 1)^4 C) 10(2x + 1)^5 D) 5(2x + 1)^5 Answer: B
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