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Derivative Rules Flashcards | StudBud

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Differentiate ag(x), where a≠e.

Differentiate csc[g(x)].

Derivative Rules

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Questions 16

Answers

1
Differentiate csc[g(x)].
csc[g'(x)]
-csc[g(x)]cot[g(x)]
-g'(x)csc[g(x)]cot[g(x)]
g'(x)csc[g(x)]cot[g(x)]
2
Differentiate a^g(x), where a≠e.
g'(x)(lna)ag(x)
g'(x)ag(x)
g'(x)(lna)ag'(x)
ag(x)
3
Differentiate u(x)v(x).
[v(x)u'(x)-u(x)v'(x)]/[v(x)]2
u'(x)v'(x)
u(x)v'(x)+v(x)u'(x)
u'(x)/v'(x)
4
Differentiate u(x)±v(x).
u(x)±v'(x)
u'(x)±v'(x)
u(x)v'(x)±v(x)u'(x)
u'(x)±v(x)
5
Differentiate sec[g(x)].
sec[g'(x)]tan[g'(x)]
sec[g(x)]tan[g(x)]
g'(x)sec[g(x)]tan[g(x)]
-g'(x)sec[g(x)]tan[g(x)]
6
Differentiate ln|g(x)|.
g'(x)/ln|g(x)|
1/ln|g(x)|
ln|g'(x)|
g'(x)/g(x)
7
Differentiate y=kf(x), where k is constant.
k
f(x)
kf(x)
kf '(x)
8
Differentiate f(x)=k, where k is constant.
0
1/k
1
k
9
Differentiate u(x)/v(x) (quotient).
u'(x)v'(x)
u'(x)/v'(x)
u(x)v'(x)+v(x)u'(x)
[v(x)u'(x)-u(x)v'(x)]/[v(x)]2
10
Differentiate cos[g(x)].
g'(x)sin[g(x)]
cos[g'(x)]
g'(x)cos[g(x)]
-g'(x)sin[g(x)]
11
Differentiate sin[g(x)].
sin[g'(x)]
cos[g'(x)]
g'(x)cos[g(x)]
g'(x)sin[g(x)]
12
Differentiate log_a|g(x)|, where a≠e.
[g'(x)lna]/g(x)
g'(x)/g(x)
g'(x)/[g(x)lna]
1/[g(x)lna]
13
Differentiate f(x)=kxⁿ, where k is constant.
k
nkxn
kxn-1
nkxn-1
14
Differentiate e^g(x).
eg'(x)
g(x)eg'(x)
eg(x)
g'(x)eg(x)
15
Differentiate tan[g(x)].
tan[g'(x)]
sec2[g(x)]
g'(x)sec2[g(x)]
sin[g(x)]/cos[g(x)]
16
Differentiate cot[g(x)].
-csc2[g(x)]
csc2[g'(x)]
-g'(x)csc2[g(x)]
g'(x)csc2[g(x)]