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Mathematics
Problem
A particle moves along the curve defined by
y
=
e
x
2
y=e^{x^{2}}
y
=
e
x
2
, where
x
x
x
depends on time according to
x
(
t
)
=
ln
(
1
+
3
t
)
x(t)=\ln(1+3t)
x
(
t
)
=
ln
(
1
+
3
t
)
. What is
d
y
d
t
\dfrac{dy}{dt}
d
t
d
y
at
t
=
2
t=2
t
=
2
? a)
6
ln
7
7
e
(
ln
7
)
2
\dfrac{6\ln 7}{7}\,e^{(\ln 7)^{2}}
7
6
ln
7
e
(
l
n
7
)
2
b)
3
ln
7
7
e
(
ln
7
)
2
\dfrac{3\ln 7}{7}\,e^{(\ln 7)^{2}}
7
3
ln
7
e
(
l
n
7
)
2
c)
6
ln
7
7
e
ln
7
\dfrac{6\ln 7}{7}\,e^{\ln 7}
7
6
ln
7
e
l
n
7
d)
6
7
e
(
ln
7
)
2
\dfrac{6}{7}\,e^{(\ln 7)^{2}}
7
6
e
(
l
n
7
)
2
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