Further Differentiation

Question 1

What is the long winded method of chain rule?

Answer 1

1. Make substitution of u=
2. Find du/dx
3. Find dy/du
4. Multiply the two together

Question 2

What is the fast way for using chain rule?

Answer 2

1. Differentiate the “inside function” and put this outside
2. Differentiate the outside function normally

Question 3

Differentiate using fast method

Answer 3

Question 4

Differentiate using fast method

Answer 4

Question 5

What is the method for product rule?

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

What’s the quotient rule?

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

What is the gradient of the inverse of a function?

Answer 11

Question 12

Answer 12

Question 13

Prove that the derivative of ln(x) is 1/x

Answer 13

Question 14

What is the derivative of a ^x?

Answer 14

ln of the base times Orginal
ln(a) a^x

Question 15

Answer 15

ln of base times k times original

Question 16

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

Answer 19

Question 20

Using implicit differentiation

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Answer 24