Differentiation Flashcards
1
Q
What is the chain rule?
A
dy/dx = dy/du x du/dx
2
Q
What is the quotient rule?
A
dy/dx =
v^2
3
Q
If y=e^x, dy/dx = ?
A
e^x
4
Q
For y= e^2x…
A
Use the chain rule.
u=2x du/dx = 2
y=e^u dy/du = e^u
dy/dx = 2e^u = 2e^2x
5
Q
If y=sinx, dy/dx = ?
A
cosx
6
Q
If y=cosx, dy/dx = ?
A
-sinx
7
Q
sinx»_space; cosx»_space; -sinx»_space; ?»_space; ?
A
sinx»_space; cosx»_space; -sinx»_space; -cosx»_space; sinx
8
Q
If y=tanx, dy/dx = ?
A
y = sinx/cosx
Use quotient rule:
u= sinx du/dx = cosx v= cosx dv/dx = -sinx
dy/dx= cos^2x + sin^2x = 1
——————- ———–
cos^2x cos^2x
=sec^2x
9
Q
What is the product rule?
A
If y=uv
dy/dx = u(dv/dx) + v(du/dx)