Derivatives of Reciprocal Trig Functions
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find
d
/
d
x
d/dx
d
/
d
x
for
f
(
x
)
=
sec
(
sin
(
x
)
)
f(x) = \sec(\sin(x))
f
(
x
)
=
sec
(
sin
(
x
))
.
QUESTION
Determine
d
/
d
x
d/dx
d
/
d
x
for
h
(
x
)
=
csc
(
2
x
)
h(x) = \csc(2x)
h
(
x
)
=
csc
(
2
x
)
.
QUESTION
Find the derivative of
h
(
x
)
=
csc
(
ln
(
x
)
)
h(x) = \csc(\ln(x))
h
(
x
)
=
csc
(
ln
(
x
))
.
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ANSWER
−
1
x
csc
(
ln
(
x
)
)
cot
(
ln
(
x
)
)
-\frac{1}{x}\csc(\ln(x))\cot(\ln(x))
−
x
1
csc
(
ln
(
x
))
cot
(
ln
(
x
))
. Chain rule: multiply by derivative of
ln
(
x
)
\ln(x)
ln
(
x
)
which is
1
x
\frac{1}{x}
x
1
.
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