Question

explane the chain rule and give the examples

Answer 1

the chain rule is a rule differentiating the composits of a function. example: Let f(x)=exf(x)=ex and g(x)=3x2+2g(x)=3x2+2. Use the chain rule to calculate h′(x)h′(x), where h(x)=f(g(x))h(x)=f(g(x)).
Solution: The derivatives of ff and gg are
f′(x)g′(x)=ex=6x.
f′(x)=exg′(x)=6x.
According to the chain rule,
h′(x)=f′(g(x))g′(x)=f′(3x2+2)(6x)=6xe3x2+2