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Chain rule/R/x^2+5x-2 over x+1 and y-2 over y^2+3/Confirm/Exercise
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Let
f
(
x
)
=
x
2
+
5
x
−
2
x
+
1
{\displaystyle {}f(x)={\frac {x^{2}+5x-2}{x+1}}\,}
and
g
(
y
)
=
y
−
2
y
2
+
3
.
{\displaystyle {}g(y)={\frac {y-2}{y^{2}+3}}\,.}
Determine the derivative of the composite
h
(
x
)
=
g
(
f
(
x
)
)
{\displaystyle {}h(x)=g(f(x))\,}
directly and by the chain rule.
Create a solution