Derivative Notation
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find the derivative of
f
(
x
)
=
1
3
x
3
f(x) = \frac{1}{3}x^3
f
(
x
)
=
3
1
x
3
.
QUESTION
Find the derivative of
f
(
x
)
=
ln
(
sin
x
)
f(x) = \ln(\sin x)
f
(
x
)
=
ln
(
sin
x
)
.
QUESTION
Find the derivative of
f
(
x
)
=
x
3
f(x) = \sqrt{x^3}
f
(
x
)
=
x
3
.
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ANSWER
f
′
(
x
)
=
3
2
x
1
/
2
f'(x) = \frac{3}{2}x^{1/2}
f
′
(
x
)
=
2
3
x
1/2
. Rewrite
x
3
=
x
3
/
2
\sqrt{x^3} = x^{3/2}
x
3
=
x
3/2
and use power rule.
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