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Mathematics
Mathematics
Problem
People living at Mars define the derivative of
f
(
x
)
f(x)
f
(
x
)
in an unusual manner as
D
∗
f
(
x
)
=
lim
h
→
0
f
2
(
x
+
h
)
−
f
2
(
x
)
h
D^*f(x)=\lim_{h\to 0}\frac{f^2(x+h)-f^2(x)}{h}
D
∗
f
(
x
)
=
lim
h
→
0
h
f
2
(
x
+
h
)
−
f
2
(
x
)
where
D
∗
f
(
x
)
D^*f(x)
D
∗
f
(
x
)
denotes the derivative of
f
(
x
)
f(x)
f
(
x
)
at Mars.
D
∗
(
tan
x
)
D^*(\tan x)
D
∗
(
tan
x
)
is equal to (a)
sec
2
x
\sec^2 x
sec
2
x
(b)
2
sec
2
x
2\sec^2 x
2
sec
2
x
(c)
tan
x
sec
2
x
\tan x\sec^2 x
tan
x
sec
2
x
(d)
2
tan
x
sec
2
x
2\tan x\sec^2 x
2
tan
x
sec
2
x
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