Solution to Review Problems for Midterm II
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چکیده
5 . (b) Applying the product rule, we have ((1 + 4x)e−4x)′ = (1 + 4x)′e−4x + (1 + 4x)(e−4x)′ = 4e−4x + (1 + 4x)e−4x(−4x)′ = 4e−4x + (1 + 4x)e−4x(−4) = 4e−4x − 4e−4x − 16xe−4x = −16xe−4x. (c) [(sec(x) + tan(x))3]′ = 3(sec(x) + tan(x))(sec(x) + tan(x))′ = 3(sec(x) + tan(x))(sec(x) tan(x) + sec(x)) = 3(sec(x) + tan(x)) · sec(x) · (sec(x) + sec(x)) = 3 sec(x)(sec(x) + tan(x)). (d)(x cos(x)− 6x sin(x)− 6 cos(x))′ = (x cos(x))′− (6x sin(x))′− (6 cos(x))′ = 5x cos(x) + x(− sin(x)) − 6 sin(x) − 6x cos(x) − 6(− sin(x)) = 5x cos(x) − x sin(x)− 6 sin(x)− 6x cos(x) + 6 sin(x) = 5x cos(x)− x sin(x)− 6x cos(x).
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