Differentiation

Question 1

State the derivatives of trig functions without constants.

Answer 1

d(sin x)/dx = cos x

d(cos x)/dx = -sin x

d(tan x)/dx = sec2 x

Question 2

State the derivatives of trig function WITH constants.

Answer 2

d(sin kx)/dx = k cos(kx)

d(cos kx)/dx = -k sin(kx)

d(tan kx)/dx = k sec2(kx)

Question 3

What are the 4 steps of the chain rule?

Answer 3

1. Choose new variable u.
2. Rewrite function with the new variable.
3. Find the two derivatives of the function and variable.
4. Multiply together.

Question 4

State the chain rule.

Answer 4

df/dx = df/du x du/dx

Question 5

State the inverse rule.

Answer 5

dx/dy = 1/(dy/dx)

Question 6

When do we use the inverse rule?

Answer 6

When it is too difficult to write y = , yet it is straight forward to differentiate for the other function.