Differentiation year 2

Question 1

How do you differentiate exponentials?

Answer 1

y = e^f(x)
dy/dx = f’(x)e^f(x)

Question 2

How do you differentiate logs (ln)?

Answer 2

y = ln (f(x))
dy/dx = f’(x)/f(x)

Question 3

How do you differentiate a^x?

Answer 3

y =a^x
dy/dx = a^xIn(a)

Question 4

What is the Chain Rule?

Answer 4

y = (2x+1)^a
bring the power to the front, take one off of the power and multiple the differentiation of the brackets
dy/dx = a(2x+1)^(a-1)(2)

Question 5

What is the differentiation order for trig?

Answer 5

sin
cos
-sin
-cos
down = differentiation
up = integration

Question 6

What is the product rule?

Answer 6

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

Question 7

What is the quotient rule?

Answer 7

y= u/v
dy/dx = (v(du/dx) - u(dv/dx))/v^2

Question 8

What is explicit and implicit formulas?

Answer 8

explicit is y=
implicit you have to rearrange for y

Question 9

What is implicit differentiation and when do you do it?

Answer 9

differentiating formula that aren’t y= (implicit formulas)
when you differentiate any value of y, multiply it by dy/dx
e.g. y^2 –> 2y dy/dx
then rearrange for dy/dx

Question 10

How do you solve Differential equations?

Answer 10

dy/dx = xy
put the x’s on one side and the y’s on another
dy 1/y = x dx
integrate both sides
solve for y

Question 11

What is the difference between a general and a particular equation?

Answer 11

general - more than one unknown values
particular - only one unknown value (usually x)