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calculus
Basic idea
Study of continuous change via limits, derivatives (rates) and integrals (accumulation).
Key formulas
Derivative:
f
′
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}
f
′
(
x
)
=
lim
h
→
0
h
f
(
x
+
h
)
−
f
(
x
)
Fundamental theorem:
∫
a
b
f
′
(
x
)
d
x
=
f
(
b
)
−
f
(
a
)
\int_a^b f'(x)\,dx=f(b)-f(a)
∫
a
b
f
′
(
x
)
d
x
=
f
(
b
)
−
f
(
a
)
Chain rule:
(
f
∘
g
)
′
(
x
)
=
f
′
(
g
(
x
)
)
g
′
(
x
)
(f\circ g)'(x)=f'(g(x))\,g'(x)
(
f
∘
g
)
′
(
x
)
=
f
′
(
g
(
x
))
g
′
(
x
)
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