# 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) = ?"

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).)
$f\left(x\right)=71{e}^{0.2x}$
{g(h), h(x)} = ?
f'(x) = ?"
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sovienesY
The given function can be decomposed into two functions, the outer function will be,
$g\left(h\right)=71{e}^{h}$
and the inner function will be,
$h\left(x\right)=0.2x$
so when we compose these function we get the composite function,
$f\left(x\right)=goh\left(x\right)=71{e}^{0.2x}$
The formula for differentiation of composite function is,
$f\prime \left(x\right)=g\prime \left(h\left(x\right)\right)·h\prime \left(x\right)$
substitute $g\left(h\right)=71{e}^{h}$ and $h\left(x\right)=0.2x$ into the formula,
${f}^{\prime }\left(x\right)=\frac{d}{dh\left(x\right)}\left(71{e}^{h\left(x\right)}\right)\cdot \frac{x}{dx}\left(0.2x\right)$
$=71{e}^{h\left(x\right)}\cdot 0.2$
$=14.2{e}^{0.2x}$
hence the differentiation of f(x) is $14.2{e}^{0.2x}.$