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Quotient rule/R/Power in denominator/Exercise
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Let
g
,
h
:
R
⟶
R
+
{\displaystyle g,h\colon \mathbb {R} \longrightarrow \mathbb {R} _{+}}
denote
differentiable functions
, and set
f
(
x
)
:=
g
(
x
)
h
(
x
)
n
,
{\displaystyle {}f(x):={\frac {g(x)}{h(x)^{n}}}\,,}
n
∈
N
+
{\displaystyle {}n\in \mathbb {N} _{+}}
.
Show that the derivative of
f
{\displaystyle {}f}
can be written as a fraction, with
h
n
+
1
(
x
)
{\displaystyle {}h^{n+1}(x)}
as denominator.
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