If y = (x – 1)(2x + 3)(sec x); evaluate y'.
Strategy # 1 - multiply out 1st, then differentiate:
y = (2x^2 + x – 3)(sec x) = 2x^2(sec x) + x(sec x) – 3(sec x)
y' = 2x^2(sec x)(tan x) + 4x(sec x) + x(sec x)(tan x) + (sec x) – 3(sec x)(tan x).
Strategy # 2 - use the product rule, then segregate and recombine like terms:
y' = (x – 1)(2x + 3)(sec...
If the function “cos sqrt(x) dx” has to be integrated, would you consider using the substitution method?
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