y=cos(x^2-3x)
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Answered by
0
Answer:
ffffffffffftttthhhhhhhhhh
Answered by
0
Answer:
The chain rule is useful whenever you have nested functions, meaning something that looks like this;
y
=
f
(
g
(
x
)
)
The chain rule tells us;
d
d
x
f
(
g
(
x
)
)
=
f
'
(
g
(
x
)
)
g
'
(
x
)
In this case, we have three nested functions;
y
=
f
(
g
(
h
(
x
)
)
)
Where;
f
=
g
2
g
=
cos
(
h
)
h
=
x
2
−
3
x
Plug each function into the one above it to see that you get the original function. To solve, use the chain rule first on
f
.
f
'
(
g
)
=
2
g
⋅
g
'
Now we use the chain rule again to solve for
g
'
.
g
'
(
h
)
=
−
sin
(
h
)
⋅
h
'
And when we solve for
h
'
via power rule;
h
'
(
x
)
=
2
x
−
3
Now just plug in
f
,
f
'
,
g
,
g
'
,
h
, and
h
'
and you get;
f
'
(
x
)
=
2
cos
(
x
2
−
3
x
)
(
−
sin
(
x
2
−
3
x
)
(
2
x
−
3
)
)
=
(
6
−
4
x
)
sin
(
x
2
−
3
)
cos
(
x
2
−
3
)
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