1.2 Deriveringsregler - Förberedande kurs i matematik 2

SolutionToHomework02.pdf

• Amplitude = 3. • Curve is flipped over the x-axis. • Period is 2π/b = 2π/2π = 1. Lös ekvationen sinx=21.

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Exempel 2. Bestäm derivatan a) b  2. Trigonometriska likheter. (1) sin(x + y) = sin x cos y + cosxsin y. (2) cos(x + y) cos2x = cos x - sinx = 2 cos' x-1=1-2 sin?

1 + x2 dx. 9.

Graphs of sine and cosine functions x 0 2π Sinx Cosx

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11. Derivatan för trigonometriska funktioner – Lektor Lindell

1 + cos x. 2 sin(x 소 y) = sin x cos y 소 cos x sin y sin x 소 sin y = 2 sin x 소 y. 2 cos x 干 y. 2 cos(x 소 y) = cos x cos y 干 sin x sin y cos x - cos y = -2 sin x + y.

1 sin x dx= 2.. 2. Let f x ={2 x 1,0 x 1. 4−x2 , 1 x 2 . Discuss the (a)  ln(x / y) = ln x - ln y ln xa = a ln x \endalignat. hvor x, y > 0.
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Let y = 3x/(2 + sinx). Then dy/  def f(x): return sin(x^3+2*x)*cos(3*x+5) diff(f(x),x,6) + 2*x) + 1620*(3*x^2 + 2)^2*x^2*cos(3*x + 5)*sin(x^3 + 2*x) - 1080*(3*x^2 + 2)^3*x*sin(x^3 + 2*x)*sin(3*x  Example6: Find: òx2 sinx dx. We use : òu .

2 sin 4x sin 2x. 4. cos 3x cos 5x. Ź (200s (u-vi-cos(utus].
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Difficult trigonometric integral Bengts funderingar

In xdx = x In x – dx = x In X – X+C u= arctan x, du = , dy = 1, V = x.

1 Primitiva funktioner

sin x = (e ix - e-ix) / 2i: Inverse sine function. The arcsine of x is defined as the inverse sine function of x when -1≤x≤1. When the sine of y is equal to x: sin y = x. Then the arcsine of x is equal to the inverse sine function of x, which is equal to y: arcsin x = sin-1 (x) = y. See: Arcsin function.

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