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Mathematics
Mathematics
Problem
Which of the following gives
d
2
d
x
2
[
f
(
x
)
g
(
x
)
]
\dfrac{d^{2}}{dx^{2}}\big[f(x)g(x)\big]
d
x
2
d
2
[
f
(
x
)
g
(
x
)
]
in terms of derivatives of
f
f
f
and
g
g
g
? a)
f
′
′
(
x
)
g
′
(
x
)
+
f
′
(
x
)
g
′
′
(
x
)
f''(x)g'(x)+f'(x)g''(x)
f
′′
(
x
)
g
′
(
x
)
+
f
′
(
x
)
g
′′
(
x
)
b)
2
f
′
(
x
)
g
′
(
x
)
2f'(x)g'(x)
2
f
′
(
x
)
g
′
(
x
)
c)
f
′
′
(
x
)
g
(
x
)
+
2
f
′
(
x
)
g
′
(
x
)
+
f
(
x
)
g
′
′
(
x
)
f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x)
f
′′
(
x
)
g
(
x
)
+
2
f
′
(
x
)
g
′
(
x
)
+
f
(
x
)
g
′′
(
x
)
d)
f
′
′
(
x
)
g
(
x
)
+
f
′
(
x
)
g
′
(
x
)
+
f
(
x
)
g
′
′
(
x
)
f''(x)g(x)+f'(x)g'(x)+f(x)g''(x)
f
′′
(
x
)
g
(
x
)
+
f
′
(
x
)
g
′
(
x
)
+
f
(
x
)
g
′′
(
x
)
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