Differentiation

Question 1

What is the differentiation of sinkx?

Answer 1

kCosx

Question 2

What is the differentiation of coskx?

Answer 2

-kSinkx

Question 3

What is the small angle approximation for sinx?

Answer 3

x

Question 4

What is the small angle approximation for cosx?

Answer 4

1-x²/2

Question 5

What is the differentiation for e^kx?

Answer 5

ke^kx

Question 6

What is the differentiation for lnx?

Answer 6

1/x

Question 7

What is the differentiation of a^kx?

Answer 7

a^kx klna

Question 8

What is the chain rule?

Answer 8

dy/dx = dy/du x du/dx

Question 9

When is the change rule used?

Answer 9

When a function is in another function or a function to a power

Question 10

What is the product rule?

Answer 10

If f(x) = g(x)h(x) , then f′(x) = g(x)h′(x) + h(x)g′(x)

Question 11

When is the product rule used?

Answer 11

When a function is multiplied by another function

Question 12

What is the quotient rule?

Answer 12

If f(x) = g(x)/h(x) , then f′(x) = h(x)g′(x) - g(x)h′(x)/(h(x))²

Question 13

When is the quotient rule used?

Answer 13

When a function is divided by another function

Question 14

What is the equation for parametric differentiation?

Answer 14

dy/dx = dy/dt // dx/dt

Question 15

How do you find a point of inflection?

Answer 15

By showing that f″(x) = 0

Question 16

State 2 explicit equations

Answer 16

• y = f(x)
• x = f(y)

Question 17

State the implicit equation for the chain rule

Answer 17

d/dx(f(y)) = f′(y)dy/dx

Question 18

State 2 implicit equations

Answer 18

• d/dx(y^n) = ny^n-1 dy/dx