Find d/dx [sin(ax + b)], where a and b are constants.
Model Answer & Options
Source: Extra Practicecos(ax + b)
a * cos(ax + b)
-a * cos(ax + b)
a * sin(ax + b)
Explanation
Using the Chain Rule, we differentiate the outer function sin(u) to get cos(u), and then multiply by the derivative of the inner function (ax + b), which is 'a'. Thus, result = a * cos(ax + b). Option A misses the inner derivative 'a'. Option C incorrectly adds a negative sign (derivative of sine is positive cosine). Option D fails to differentiate the sine function.
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