Differentiation:-

Question 1

DY/DX X^n

Answer 1

nX^(n-1)

Question 2

DY/DX e^x

Answer 2

e^x

Question 3

DY/DX ke^x

Answer 3

ke^x

Question 4

DY/DX lnx

Answer 4

1/x

Question 5

DY/DX klnx

Answer 5

k/x

Question 6

DY/DX e^(ax)

Answer 6

ae^(ax)

Question 7

DY/DX e^(f(x))

Answer 7

f’(x)e^(f(x))

Question 8

DY/DX ln(ax)

Answer 8

1/x

Question 9

DY/DX ln(f(x))

Answer 9

(f’(x))/(f(x))

Question 10

DY/DX sinx

Answer 10

cosx

Question 11

DY/DX cosx

Answer 11

-sinx

Question 12

DY/DX tanx

Answer 12

(1/((cos^2)x))

Question 13

DY/Dx sinkx

Answer 13

kcoskx

Question 14

Dy/dx coskx

Answer 14

-ksinkx

Question 15

Chain rule:-

Answer 15

Y= function within a function. Dy/dx = dy/du x du/dx. Bring down power, reduce by 1 then multiply by derivative of bracket. U = inside the bracket.

Question 16

Product rule:-

Answer 16

Y= UV
Dy/dx = v (du/dx) + u (du/dx)

Question 17

Quotient rule:-

Answer 17

Y = u/v
Dy/dx = (v (du/dx) - u (dv/dx))/V^2