Differentiation

Question 1

y = ax^n

Find dy/dx

Answer 1

dy/dx = anx^n-1

Question 2

What’s the formula for differentiation from 1st principles

Answer 2

f ‘ (x) = lim h tend to 0
[ { f(x+h) - f(x) } / h]

Question 3

What’s a stationary point?

Answer 3

The points on a function where its derivative is 0

Question 4

How do you find the stationary points of a graph?

Answer 4

Differentiate the function.

Set this derivative equal to zero.

Solve for 𝑥.

Substitute the 𝑥 coordinates back into the function to find the y coordinates.

Question 5

What is the formula for chain rule if y = f(x)^n?

Answer 5

dy/dx = nf(x)^-1 * f ‘ (x)

Question 6

What’s the second version of chain rule if there are three variables?

Answer 6

dy/dx = dv/dx * dy/dv

Question 7

What’s the product rule? (if y = uv)

Answer 7

dy/dx = u dv/dx + vdu/dx

Question 8

What’s the quotient rule? (if y = uv)

Answer 8

dy/dx = (vu’ - v’u) / v^2

Question 9

What is the inverse function of sin(x)

Answer 9

sec(x)

Question 10

What is the value of sec(x)

Answer 10

1/sin(x)

Question 11

What is the inverse function of cos(x)

Answer 11

cosec(x)

Question 12

What is the value of cosec(x)

Answer 12

1/cos(x)

Question 13

What is the inverse function of tan(x)

Answer 13

cot(x)

Question 14

What is the value of cot(x)

Answer 14

1/tan(x)

Question 15

What’s the derivative of sin(x)

Answer 15

cos(x)

Question 16

What’s the derivative of tan(x)

Answer 16

sec^2(x)

Question 17

What’s the derivative of cos(x)

Answer 17

-sin(x)

Question 18

What’s the derivative of ln(x)

Answer 18

1/x

Question 19

What’s the derivative of (a^kx)

Answer 19

a^kx(klna)

Question 20

What’s the derivative of (e^kx)

Answer 20

ke^kx