Differentiation and Integration of other Functions Flashcards
1
Q
y = ln(f(x))
A
dy/dx = f’(x)/f(x)
2
Q
y = e^f(x)
A
dy/dx = f’(x)e^f(x)
3
Q
y = a^f(x)
A
dy/dx = f’(x)a^f(x) * lna
4
Q
y = sin(f(x))
A
dy/dx = f’(x)cos(f(x))
5
Q
y = cos(f(x))
A
dy/dx = -f’(x)sin(f(x))
6
Q
y = tan(f(x))
A
dy/dx = f’(x)sec^2(f(x))
7
Q
∫[sin(ax+b)]dx
A
y = (-1/a)cos(ax+b) + C
8
Q
∫[cos(ax+b)]dx
A
y = (1/a)sin(ax+b) + C
9
Q
∫[sec^2(ax+b)]dx
A
y = (1/a)tan(ax+b) + C
10
Q
∫[e^(ax+b)]dx
A
y = (1/a)e^(ax+b) + C
11
Q
∫[1/(ax+b)]dx
A
y = (1/a)ln|(ax+b)| + C
12
Q
∫[f’(x)/f(x)]dx
A
y = ln|f(x)| + C
13
Q
y = uv
A
dy/dx = uv’ + vu’
14
Q
y = u/v
A
dy/dx = (vu’ - uv’)/v^2
