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Differentiation Rules for Products, Quotients, Secants, and Tangents

Learn how to apply the product rule, quotient rule, and differentiate trigonometric functions with step-by-step examples. Understand how to find derivatives efficiently for various functions.

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Differentiation Rules for Products, Quotients, Secants, and Tangents

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  1. 2.3 Differentiation Rules for Products, Quotients, Secants, and Tangents

  2. Product Rule The 1st times the der. of the 2nd + the 2nd times the der. of the 1st. uv’+vu’ Ex. f(x) = (3x – 2x2)(5 + 4x) f’(x) = (3x – 2x2) (4) + (5 + 4x) (3 – 4x) f’(x) = 12x – 8x2 + 15 – 20x + 12x – 16x2 f’(x) = -24x2 + 4x + 15

  3. x cos x + sin x (1) = x cos x + sin x y = 2x cos x – 2 sin x y’ = (2x)(-sin x) + cos x (2) - 2 cos x = -2x sin x Quotient Rule

  4. Differentiate (2 – 3x) (4x – 4) - (2x2 – 4x + 3) (-3) y’ = (-12x2 + 20x – 8) – (- 6x2 + 12x – 9) y’ = -6x2 + 8x + 1 y’ =

  5. Derivatives of Trigonometric Functions Differentiate y = x – tan x y = x sec x y’ = x(sec x tan x) + (sec x)(1) y’ = sec x(x tan x + 1)

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