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Mathematics
Problem
Which of the following gives the derivative of a function
f
f
f
at
x
=
a
x=a
x
=
a
according to the limit definition? a)
f
′
(
a
)
=
lim
h
→
0
f
(
a
)
−
f
(
a
+
h
)
h
f'(a)=\displaystyle\lim_{h\to 0}\frac{f(a)-f(a+h)}{h}
f
′
(
a
)
=
h
→
0
lim
h
f
(
a
)
−
f
(
a
+
h
)
b)
f
′
(
a
)
=
lim
h
→
a
f
(
a
+
h
)
−
f
(
a
)
h
f'(a)=\displaystyle\lim_{h\to a}\frac{f(a+h)-f(a)}{h}
f
′
(
a
)
=
h
→
a
lim
h
f
(
a
+
h
)
−
f
(
a
)
c)
f
′
(
a
)
=
lim
x
→
a
f
(
x
)
−
f
(
a
)
x
−
a
f'(a)=\displaystyle\lim_{x\to a}\frac{f(x)-f(a)}{x-a}
f
′
(
a
)
=
x
→
a
lim
x
−
a
f
(
x
)
−
f
(
a
)
d)
f
′
(
a
)
=
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
a
f'(a)=\displaystyle\lim_{h\to 0}\frac{f(a+h)-f(a)}{a}
f
′
(
a
)
=
h
→
0
lim
a
f
(
a
+
h
)
−
f
(
a
)
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