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Question

Differentiate the function with respect to x
sin(ax+b)cos(cx+d)

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Solution

We have, f(x)=sin(ax+b)cos(cx+d)
Thus using quotient rule and chain rule simualtaneously,
f(x)=acos(ax+b).cos(cx+d)sin(ax+b)(csin(cx+d))[cos(cx+d)]2
=acos(ax+b)cos(cx+d)+csin(ax+b).sin(cx+d)cos(cx+d)×1cos(cx+d)
=acos(ax+b)sec(cx+d)+csin(ax+b)tan(cx+d)sec(cx+d)

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