Derivatives Of Standard Functions
Akopọ
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.
Awọn Afojusun
- 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.
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- 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
O wa lori ohun elo Green Bridge
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O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
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