Chp 5:PD 1

Question 1

Dy/dx of y= a^x

Answer 1

Dy/dx= a^x ln a

Question 2

Dy/dx of x^n

Answer 2

Dy/dx= nx^n-1

Question 3

Dy/dx of e^x

Answer 3

Dy/dx= e^x

Question 4

Dy/dx of e^kx

Answer 4

Dy/dx = ke^kx

Question 5

Dy/dx of ln x

Answer 5

Dy/dx = 1/x

Question 6

Dy/dx of log lc(a) x

Answer 6

Dy/dx = 1/ x ln a

Question 7

Dy/dx of sin x

Answer 7

Dy/dx = cos x

Question 8

Dy/dx of cos x

Answer 8

Dy/dx = - sin x

Question 9

Dy/dx of tan x

Answer 9

Dy/dx = sec^2 x

Question 10

Dy/dx of cot x

Answer 10

Dy/dx = -csc^2 x

Question 11

Dy/dx of sec x

Answer 11

Dy/dx = sec x tan x

Question 12

Dy/dx of csc x

Answer 12

-csc x cot x

Question 13

Dy/dx of sinh x

Answer 13

Cosh x

Question 14

Dy/dx of cosh x

Answer 14

Sinh x

Question 15

Chain rule

Answer 15

Dy/dx = dy/du x du/dx

Question 16

Product rule

Answer 16

Dy/dx = udv/dx + vdu/dx

Question 17

Quotient rule

Answer 17

Dy/dx = vdu/dx - udv/dx / v^2

Question 18

Dy/dx of coth x

Answer 18

-csch^2 x

Question 19

Dy/dx of csch x

Answer 19

• csch x coth x

Question 20

Dy/dx of Sech x

Answer 20

• sech x tanh x

Question 21

Dy/dx of tanh x

Answer 21

Sech^2 x

Question 22

Dy/dx of cos^-1 x

Answer 22

-1/(1-x^2)^1/2

Question 23

Dy/dx of sin^-1 x

Answer 23

1/(1-x^2)^1/2