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Mathematics
Mathematics
Problem
Let
H
(
x
)
=
∫
1
cos
x
e
t
2
d
t
+
∫
x
4
e
t
2
d
t
H(x)=\displaystyle\int_{1}^{\cos x} e^{t^{2}}\,dt+\int_{x}^{4} e^{t^{2}}\,dt
H
(
x
)
=
∫
1
c
o
s
x
e
t
2
d
t
+
∫
x
4
e
t
2
d
t
. What is
H
′
(
x
)
H'(x)
H
′
(
x
)
? a)
sin
x
e
(
cos
x
)
2
−
e
x
2
\sin x\,e^{(\cos x)^{2}}-e^{x^{2}}
sin
x
e
(
c
o
s
x
)
2
−
e
x
2
b)
−
sin
x
e
(
cos
x
)
2
+
e
x
2
-\sin x\,e^{(\cos x)^{2}}+e^{x^{2}}
−
sin
x
e
(
c
o
s
x
)
2
+
e
x
2
c)
−
sin
x
e
(
cos
x
)
2
−
e
x
2
-\sin x\,e^{(\cos x)^{2}}-e^{x^{2}}
−
sin
x
e
(
c
o
s
x
)
2
−
e
x
2
d)
−
sin
x
e
x
2
−
e
x
2
-\sin x\,e^{x^{2}}-e^{x^{2}}
−
sin
x
e
x
2
−
e
x
2
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