For the composite function, identify an inside function and an oposite fnction abd write the derivative with respect to x of the composite function. (The function is of the form f(x)=g(h(x)). Use non-identity dunctions for g(h) and h(x).) f(x)=71e^(0.2x) {g(h), h(x)} = ? f'(x) = ?"

Dottie Parra 2021-02-06 Answered
For the composite function, identify an inside function and an oposite fnction abd write the derivative with respect to x of the composite function. (The function is of the form f(x)=g(h(x)). Use non-identity dunctions for g(h) and h(x).)
f(x)=71e0.2x
{g(h), h(x)} = ?
f'(x) = ?"
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Expert Answer

sovienesY
Answered 2021-02-07 Author has 89 answers
The given function can be decomposed into two functions, the outer function will be,
g(h)=71eh
and the inner function will be,
h(x)=0.2x
so when we compose these function we get the composite function,
f(x)=goh(x)=71e0.2x
The formula for differentiation of composite function is,
f(x)=g(h(x))·h(x)
substitute g(h)=71eh and h(x)=0.2x into the formula,
f(x)=ddh(x)(71eh(x))xdx(0.2x)
=71eh(x)0.2
=14.2e0.2x
hence the differentiation of f(x) is 14.2e0.2x.
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