Correct Answer - Option 2 : 3 cos (3x + 2) + 3
Concept:
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\(\rm d\over dx\)xn = nxn-1
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\(\rm d\over dx\)sin x = cos x
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\(\rm d\over dx\)cos x = -sin x
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\(\rm d\over dx\)ex = ex
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\(\rm d\over dx\)ln x = \(\rm1\over x\)
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\(\rm d\over dx\)tan x = sec2 x
Chain Rule: If y is a function of u and u is a function of x
- \(\rm {dy\over dx} = {dy\over du}\times {du\over dx}\)
Calculation:
y(x) = sin (3x + 2) + 3x
y'(x) = \(\rm d\over dx\)[sin (3x + 2) + 3x]
y'(x) = \(\rm d\over dx\)sin (3x + 2) + \(\rm d\over dx\)3x
y'(x) = cos(3x + 2) \(\rm d\over dx\) (3x + 2) + 3
y'(x) = cos(3x + 2) (3x) + 3
y'(x) = 3x cos(3x + 2) + 3
