Differentiation

Question 1

What is the chain rule?

Answer 1

dy/dx = dy/du x du/dx

Question 2

What is the quotient rule?

Answer 2

dy/dx =

      v^2

Question 3

If y=e^x, dy/dx = ?

Answer 3

e^x

Question 4

For y= e^2x…

Answer 4

Use the chain rule.

u=2x du/dx = 2

y=e^u dy/du = e^u

dy/dx = 2e^u = 2e^2x

Question 5

If y=sinx, dy/dx = ?

Answer 5

cosx

Question 6

If y=cosx, dy/dx = ?

Answer 6

-sinx

Question 7

sinx»_space; cosx»_space; -sinx»_space; ?»_space; ?

Answer 7

sinx»_space; cosx»_space; -sinx»_space; -cosx»_space; sinx

Question 8

If y=tanx, dy/dx = ?

Answer 8

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

Question 9

What is the product rule?

Answer 9

If y=uv

dy/dx = u(dv/dx) + v(du/dx)