Differentiation - 10

Question 1

what does Asinx differentiate to?

Answer 1

Acosx

Question 2

what does Acosx differentiate to?

Answer 2

-Asinx

Question 3

what does Atanx differentiate to?

Answer 3

Asec^2x

Question 4

what does Alnx differentiate to?

Answer 4

A/x

Question 5

what does Ae^x differentiate to?

Answer 5

dy/dx = Ae^x

Question 6

how to differentiate sin(A+B) from first principles

Answer 6

sinAcosB + cosAsinB and then

Question 7

how to differentiate cos(A+B) from first principles

Answer 7

cosAcosB - sinAsinB

Question 8

What is the derivative of e^f(x)?

Answer 8

f’(x)e^f(x)

Question 9

What is the derivative of ln f(x) ?

Answer 9

f’(x) / f(x)

Question 10

What is the derivative of cos kx?

Answer 10

-ksin kx

Question 11

What is the derivative of tan kx?

Answer 11

ksec2 kx

Question 12

What is the derivative of cosec x?

Answer 12

-cosecx cotx

Question 13

What is the derivative of cosec kx?

Answer 13

-k coseckx cot kx

Question 14

What is the derivative of sec x?

Answer 14

secx tanx

Question 15

What is the derivative of sec kx?

Answer 15

sec x tan x

Question 16

What is the derivative of cotx?

Answer 16

-cosec^2 x

Question 17

What is the derivative of a^kx?

Answer 17

k ln(a) a^x

Question 18

What is the derivative of lnxn?

Answer 18

1/x

Question 19

What is the chain rule? and when do you use it

Answer 19

subsitute T for in the brackets. dy/dt x dt/dx

use when f(x)^n

Question 20

derivative of arcsec

Answer 20

1/ x root x^2 -1

Question 21

derivative of arc cot x?

Answer 21

-1/1+x^2

Question 22

derivative of arcsec x

Answer 22

1/ x root x^2 -1

Question 23

derivatives of arc cosec x

Answer 23

-1 / x root x^2 -1

Question 24

derivative of loga(x)

Answer 24

1 / (x ln(a))

Question 25

how do you differentiate using the product rule

Answer 25

du/dx V x dv/dx U