Question

Answer the differentiation question

Answer 1

f(x)=sin(x)cos(x)g(x)=csc(x)f(x)=sin(x)cos(x)g(x)=csc(x)

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