Derivatives Flashcards
1
Q
Y=sinx
A
Y’ =cosx
2
Q
Y=cosx
A
Y’= -sinx
3
Q
Y=tanx
A
Y’= sec^2x
4
Q
Y=cotx
A
Y’= -csc^2x
5
Q
Y=secx
A
Y’=secxtanx
6
Q
Y=cscx
A
Y’= -cscxcotx
7
Q
Product rule
A
Y’=f (x)g’(x)+g(x)f’(x)
8
Q
Quotient rule
A
Y’= (g(x)f’(x) - f(x)g’(x))/((g(x))^2)
9
Q
y=lnx
A
y’=1/x
10
Q
Y=logbX
A
Y’= 1/(xlnb)
11
Q
Y=b^x
A
Y’=b^xlnb
12
Q
Y=e^x
A
Y’=e^x
13
Q
Y=e^-x
A
Y’= -e^-x
14
Q
Sqrt(x)
A
1/(2sqrtx)
15
Q
Y=arcsinx
A
y’=1/(sqrt(1-x^2))
16
Q
Y=arccosx
A
Y’= -1/(sqrt(1-x^2))
17
Q
Y=arctanx
A
Y’=1/(1+x^2)
18
Q
Y=arccotx
A
Y’=-1/(1+x^2)
19
Q
Y=arcsecx
A
Y’=1/(|x|sqrt(x^2-1))
20
Q
Y=arccscx
A
Y’=-1/(|x|sqrt(x^2-1))
21
Q
Sinhx
A
(e^x-e^-x)/(2)
22
Q
Coshx
A
(e^x+e^-x)/(2)
23
Q
Cosh^2-sinh^2x=
A
=1
24
Q
Y=sinhx
A
Y’=coshx
25
Q
Y=coshx
A
Y’=sinhx
26
Q
Y=tanhx
A
Y’=sech^2x
27
Q
Y=cothx
A
Y’=-csch^2x
28
Q
Y=sechx
A
Y’=-tanhxsechx
29
Q
Y=cschx
A
Y’=-cothxcschx
30
Q
Y=arcsinhx
A
Y’=1/(sqrt(1+x^2))
31
Q
Y=arctanhx
A
Y’=1/(1-x^2)
