Week 11

Question 1

dydx

y= 2x⁴sin(x)

Answer 1

Question 2

dydx

y= 5xln(x)

Answer 2

Question 3

dydx

y= 4x³e^x

Answer 3

Question 4

dydx

y= (3x²−2x) cos(x)

Answer 4

Question 5

dydx

y= (3x−2)(4−x)

Answer 5

Question 6

Consider the function

y=−3x(x⁴−8)

(a) Find dydx by first expanding the function

Answer 6

Question 7

Consider the function

y=−3x(x⁴−8)

(b) Find dydx by using the product rule and show that it gives the same result as part (a)

Answer 7

Question 8

dydx

Answer 8

Question 9

dydx

Answer 9

Question 10

dydx

Answer 10

Question 11

dydx

Answer 11

Question 12

do a)

Answer 12

Question 13

B

Answer 13

Question 14

dydx

y= sin(x²)

Answer 14

Question 15

dydx

y= cos(3x−1)

Answer 15

Question 16

dydx

y= 5e^{2x^3}

Answer 16

Question 17

dydx

y= (2x−5x²)⁸

Answer 17

Question 18

dydx

y= ln(12x³)

Answer 18

Question 19

dydx

Answer 19

Question 20

What is the gradient of the curve

y= (4x−1)³

at x= 2

Answer 20

Question 21

Find the equation of the tangent to the curve

y= √2x+ 3

at x= 3

Answer 21

Question 22

A

Answer 22

Question 23

B

Answer 23

Question 24

C

Answer 24

Question 25

A

Answer 25

Question 26

B

Answer 26

Question 27

C

Answer 27

Question 28

D

Answer 28

Question 29

E

Answer 29

Question 30

A

Answer 30

Question 31

B

Answer 31

Question 32

Answer 32

Question 33

A

Answer 33

Question 34

B

Answer 34