Differentiation

Question 1

Product rule:

Answer 1

d/dx (uv) =u’v + uv’

Question 2

Sin x diffentiates to

Answer 2

cos x

Question 3

Cos x diffentiates to

Answer 3

-sin x

Question 4

Quotient rule:

Answer 4

d/dx(u/ v) = (u’v - uv’)/ v^2

Question 5

e^5x diffentiates to

Answer 5

5e^5x

Question 6

ln(x) diffentiates to

Answer 6

1/x

Question 7

Chain rule:

Answer 7

When differentiating a function within a function we must multiply by the derivative of the function

Question 8

How do terms involving y differentiate + example of 2y^2 derivative

Answer 8

Differentiate normal but multiplied by dy/dx
4y*dy/dx

Question 9

Process of implicit differentiation

Answer 9

Differentiate whole expression (both sides) - remembering rules for differentiating y and chain rule when required.
Move parts not involving dy/dx to RHS.
Take out common factor of dy/dx for remaining LHS.
Divide both sides by bracket.
Simplify fraction if required.

Question 10

Process of logarithmic differentiation

Answer 10

Take ln of both sides of equations.
Use log rules to get rid of powers.
Differentiate both sides using product rule and rule for y.
Move y to RHS.
Sub in original value for y from original equation

Question 11

Parametric differentiation (dy/dx)=

Answer 11

dy/du * du/dx or (dy/du)/(dx/du)

Question 12

Process for first order parametric differentiation

Answer 12

Differentiate two given equations with respect to (t or u) for example.
Sub equation into dy/dx = dy/du*du/dx

Question 13

Second order parametric differentiation (u)
d^2y/dx^2 =

Answer 13

d/du(dy/dx) * du/dx

Question 14

Solving second order parametric differentiations:

Answer 14

Do as normal then sub into second order parametric equation. Differentiate dy/dx then multiply by du/dx to get answer.