Diffrential calculus [all Rules] Flashcards
1
Q
d/dx [cf (x)] = ?
A
cf ′(x), c is any constant.
2
Q
d/dx (c) = ?
A
0
3
Q
d/dx [xⁿ] = ?
A
nxⁿ⁻¹
4
Q
[f(x)g(x)]’ =
A
f(x)’g(x) + f(x)g(x)’
5
Q
( f(x)÷g(x) )’ =
A
f(x)’g(x) - f(x)g(x)’ ÷ ( g(x) )²
6
Q
d/dx [ f(gx) ] = ?
A
f’(g(x)) g’(x)
7
Q
d/dx ( e^g(x) ) = ?
A
g’(x) e^g(x)
8
Q
d/dx ( ln (g(x)) ) = ?
A
g’(x) ÷ g(x)
9
Q
d/dx ( sin x ) = ?
A
cos x
10
Q
d/dx ( cos x ) = ?
A
— sin x
11
Q
d/dx tan (x) = ?
A
sec² x
12
Q
d/dx ( csc (x) ) = ?
A
— csc (x) cot (x)
13
Q
d/dx sec (x)
A
sec (x) tan (x)
14
Q
d/dx ( cot (x) )
A
— csc²(x)
15
Q
d/dx [ aˣ ] = ?
A
aˣ ln (a)
16
Q
d/dx [ ln(x) ] = ?
A
1/x , x > 0
17
Q
d/dx [ eˣ ] = ?
A
eˣ
18
Q
log ₐ (x) = ?
A
1 / xln(a) , x > 0
19
Q
sin x + sin y = ?
A
2sin ( x - y / 2 ) cos (x + y / 2)
20
Q
cos x + cos y =
A
2cos ( x + y / 2 ) cos (x - y / 2)
21
Q
cos x - cos y =
A
-2 sin ( x + y / 2 ) sin (x - y / 2 ]
22
Q
sin x - sin y
A
2sin ( x + y / 2 ) cos (x - y / 2)
