Answer the differentiation question
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y=5f(x)+4g(x)y=5f(x)+4g(x)//substitution
dydx=5f′(x)+4g′(x)dydx=5f′(x)+4g′(x) //sum of derivatives
f′(x)=(cos(x))cos(x)+sin(x)(−sin(x))f′(x)=(cos(x))cos(x)+sin(x)(−sin(x))// product rule
=cos2(x)−sin2(x)=cos2(x)−sin2(x)//simplify
g′(x)=−csc(x)cot(x)g′(x)=−csc(x)cot(x) // memory
→dydx=5(sin2(x)−cos2(x))−4csc(x)cot(x)
→dydx=5(sin2(x)−cos2(x))−4csc(x)cot(x)// final answer