Differentiation further

Question 1

f(x) = (a^x)

f’(x) =

Answer 1

(a^x)(ln(a))

Question 2

if y = e^kx

dy/dx =

Answer 2

ke^kx

Question 3

if y = lnkx

dy/dx =

Answer 3

1/x

Question 4

y = sinx

dy/dx =

Answer 4

cosx

Question 5

y= cosx

dy/dx =

Answer 5

-sinx

Question 6

y=5cosx

dy/dx =

Answer 6

-5sinx

Question 7

chain rule

Answer 7

dy/dx = dy/du x du/dx

where u is the function being subbed into the other

Question 8

dy/dx of 4y^3

Answer 8

Use chain rule

12y^2 dy/dx

Question 9

f(x) = (3^x)

f’(x) =

Answer 9

(3^x)(ln3)

Question 10

d/dx (a^kx) =

Answer 10

ka^kx(lna)

Question 11

if x is expressed as a function of y, then dy/dx =

Answer 11

1/ (dy/dx)

Question 12

point of inflection

Answer 12

changes from concave to convex

This means that a point of inflection is a point where the second derivative changes sign (from positive to negative or vice versa)

Question 13

5 steps to finding a point of inflection

starting with f(x)

Answer 13

1) Find f’(x)
2) Find f’‘(x)
3) f’‘(x) = 0
4) check f’‘(x) a bit either side to see sign of f’‘(x)
if the sign are the same, is not a POI
if the sign are different, is a POI
5) sub x value into f(x) to get corresponding y coordinate